Quick Answer
SAT conditional probability questions test reduced sample spaces, two-way tables, dependent events, independence, reverse conditions, and multi-step probability models.
What Should You Know?
- P(A | B) means the probability of A given B.
- Use B as the denominator.
- P(A | B)=P(A and B)/P(B).
- Independent events satisfy P(A | B)=P(A).
- Without replacement usually creates dependence.
In This Guide
Start With SAT Math Topic-Wise Practice
Connect conditional probability practice with weekly score planning.
Download the SAT Prep Guide E-Book
Organize conditional probability and data-analysis practice with a clear weekly plan.
Download SAT Prep Guide E-BookWhat Does the SAT Test in Conditional Probability Questions?
Students may need to reduce a sample space, read a two-way table, identify independence, or reverse a condition.
| Skill | Questions | Main Trap |
|---|---|---|
| Basics | Q1-Q15 | Original total |
| Two-way tables | Q16-Q30 | Wrong row or column |
| Dependence | Q31-Q45 | Ignoring replacement |
| Advanced | Q46-Q70 | Reverse condition |
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How Are Basic Conditional Probabilities Calculated?
Use the conditioned group as the denominator.
CONDITIONAL PROBABILITY BASICS
EASY
Question 1
Among 18 people in a specified group, 9 satisfy condition A. Given that a person is in this group, what is the probability the person satisfies A?
Which choice is correct?
A) 1/3
B) 1/2
C) 9/100
D) 2/9
Show full solution
Correct answer: B) 1/2
Use the conditioned group as the denominator: 9/18 = 1/2.
SAT trap: The condition determines the denominator.
CONDITIONAL PROBABILITY BASICS
EASY
Question 2
Among 24 people in a specified group, 18 satisfy condition A. Given that a person is in this group, what is the probability the person satisfies A?
Which choice is correct?
A) 3/7
B) 3/4
C) 1/4
D) 9/50
Show full solution
Correct answer: B) 3/4
Use the conditioned group as the denominator: 18/24 = 3/4.
SAT trap: The condition determines the denominator.
CONDITIONAL PROBABILITY BASICS
EASY
Question 3
Among 30 people in a specified group, 12 satisfy condition A. Given that a person is in this group, what is the probability the person satisfies A?
Which choice is correct?
A) 2/7
B) 2/5
C) 3/5
D) 3/25
Show full solution
Correct answer: B) 2/5
Use the conditioned group as the denominator: 12/30 = 2/5.
SAT trap: The condition determines the denominator.
CONDITIONAL PROBABILITY BASICS
EASY
Question 4
Among 40 people in a specified group, 14 satisfy condition A. Given that a person is in this group, what is the probability the person satisfies A?
Which choice is correct?
A) 7/27
B) 7/20
C) 13/20
D) 7/50
Show full solution
Correct answer: B) 7/20
Use the conditioned group as the denominator: 14/40 = 7/20.
SAT trap: The condition determines the denominator.
CONDITIONAL PROBABILITY BASICS
EASY
Question 5
Among 15 people in a specified group, 6 satisfy condition A. Given that a person is in this group, what is the probability the person satisfies A?
Which choice is correct?
A) 2/7
B) 2/5
C) 3/5
D) 3/50
Show full solution
Correct answer: B) 2/5
Use the conditioned group as the denominator: 6/15 = 2/5.
SAT trap: The condition determines the denominator.
CONDITIONAL PROBABILITY BASICS
EASY
Question 6
Among 28 people in a specified group, 21 satisfy condition A. Given that a person is in this group, what is the probability the person satisfies A?
Which choice is correct?
A) 3/7
B) 3/4
C) 1/4
D) 21/100
Show full solution
Correct answer: B) 3/4
Use the conditioned group as the denominator: 21/28 = 3/4.
SAT trap: The condition determines the denominator.
CONDITIONAL PROBABILITY BASICS
MEDIUM
Question 7
Among 20 people in a specified group, 8 satisfy condition A. Given that a person is in this group, what is the probability the person satisfies A?
Which choice is correct?
A) 2/7
B) 2/5
C) 3/5
D) 2/25
Show full solution
Correct answer: B) 2/5
Use the conditioned group as the denominator: 8/20 = 2/5.
SAT trap: The condition determines the denominator.
CONDITIONAL PROBABILITY BASICS
MEDIUM
Question 8
Among 32 people in a specified group, 20 satisfy condition A. Given that a person is in this group, what is the probability the person satisfies A?
Which choice is correct?
A) 5/13
B) 5/8
C) 3/8
D) 1/5
Show full solution
Correct answer: B) 5/8
Use the conditioned group as the denominator: 20/32 = 5/8.
SAT trap: The condition determines the denominator.
CONDITIONAL PROBABILITY BASICS
MEDIUM
Question 9
Among 50 people in a specified group, 35 satisfy condition A. Given that a person is in this group, what is the probability the person satisfies A?
Which choice is correct?
A) 7/17
B) 7/10
C) 3/10
D) 7/20
Show full solution
Correct answer: B) 7/10
Use the conditioned group as the denominator: 35/50 = 7/10.
SAT trap: The condition determines the denominator.
CONDITIONAL PROBABILITY BASICS
MEDIUM
Question 10
Among 45 people in a specified group, 27 satisfy condition A. Given that a person is in this group, what is the probability the person satisfies A?
Which choice is correct?
A) 3/8
B) 3/5
C) 2/5
D) 27/100
Show full solution
Correct answer: B) 3/5
Use the conditioned group as the denominator: 27/45 = 3/5.
SAT trap: The condition determines the denominator.
CONDITIONAL PROBABILITY BASICS
MEDIUM
Question 11
Among 36 people in a specified group, 9 satisfy condition A. Given that a person is in this group, what is the probability the person satisfies A?
Which choice is correct?
A) 1/5
B) 1/4
C) 3/4
D) 9/100
Show full solution
Correct answer: B) 1/4
Use the conditioned group as the denominator: 9/36 = 1/4.
SAT trap: The condition determines the denominator.
CONDITIONAL PROBABILITY BASICS
MEDIUM
Question 12
Among 64 people in a specified group, 16 satisfy condition A. Given that a person is in this group, what is the probability the person satisfies A?
Which choice is correct?
A) 1/5
B) 1/4
C) 3/4
D) 4/25
Show full solution
Correct answer: B) 1/4
Use the conditioned group as the denominator: 16/64 = 1/4.
SAT trap: The condition determines the denominator.
CONDITIONAL PROBABILITY BASICS
MEDIUM
Question 13
Among 25 people in a specified group, 10 satisfy condition A. Given that a person is in this group, what is the probability the person satisfies A?
Which choice is correct?
A) 2/7
B) 2/5
C) 3/5
D) 1/10
Show full solution
Correct answer: B) 2/5
Use the conditioned group as the denominator: 10/25 = 2/5.
SAT trap: The condition determines the denominator.
CONDITIONAL PROBABILITY BASICS
MEDIUM
Question 14
Among 48 people in a specified group, 30 satisfy condition A. Given that a person is in this group, what is the probability the person satisfies A?
Which choice is correct?
A) 5/13
B) 5/8
C) 3/8
D) 3/10
Show full solution
Correct answer: B) 5/8
Use the conditioned group as the denominator: 30/48 = 5/8.
SAT trap: The condition determines the denominator.
CONDITIONAL PROBABILITY BASICS
MEDIUM
Question 15
Among 60 people in a specified group, 45 satisfy condition A. Given that a person is in this group, what is the probability the person satisfies A?
Which choice is correct?
A) 3/7
B) 3/4
C) 1/4
D) 9/20
Show full solution
Correct answer: B) 3/4
Use the conditioned group as the denominator: 45/60 = 3/4.
SAT trap: The condition determines the denominator.
Build Stronger SAT Probability Skills
Connect probability with ratios, tables, and data analysis.
How Are Two-Way Tables Used?
Read row totals, column totals, and intersections carefully.
TWO-WAY TABLES
MEDIUM
Question 16
A two-way table shows Group A has 18 Yes and 6 No responses, while Group B has 12 Yes and 14 No responses. What is P(Yes | Group A)?
Which choice is correct?
A) 9/25
B) 3/4
C) 1/4
D) 2/5
Show full solution
Correct answer: B) 3/4
Use the Group A row total: 18/(18+6) = 3/4.
SAT trap: Use the row or column total named by the condition.
TWO-WAY TABLES
MEDIUM
Question 17
A two-way table shows Group A has 32 Yes and 18 No responses, while Group B has 20 Yes and 30 No responses. What is P(Group B | Yes)?
Which choice is correct?
A) 8/25
B) 5/13
C) 9/25
D) 2/9
Show full solution
Correct answer: B) 5/13
Use the Yes column total: 20/(32+20) = 5/13.
SAT trap: Use the row or column total named by the condition.
TWO-WAY TABLES
MEDIUM
Question 18
A two-way table shows Group A has 28 Yes and 7 No responses, while Group B has 36 Yes and 9 No responses. What is P(No | Group B)?
Which choice is correct?
A) 7/20
B) 1/5
C) 9/16
D) 2/9
Show full solution
Correct answer: B) 1/5
Use the Group B row total: 9/(36+9) = 1/5.
SAT trap: Use the row or column total named by the condition.
TWO-WAY TABLES
MEDIUM
Question 19
A two-way table shows Group A has 45 Yes and 30 No responses, while Group B has 30 Yes and 20 No responses. What is P(Yes | Group A)?
Which choice is correct?
A) 9/25
B) 3/5
C) 2/5
D) 2/9
Show full solution
Correct answer: B) 3/5
Use the Group A row total: 45/(45+30) = 3/5.
SAT trap: Use the row or column total named by the condition.
TWO-WAY TABLES
MEDIUM
Question 20
A two-way table shows Group A has 24 Yes and 16 No responses, while Group B has 30 Yes and 10 No responses. What is P(Group B | Yes)?
Which choice is correct?
A) 3/10
B) 5/9
C) 2/5
D) 2/9
Show full solution
Correct answer: B) 5/9
Use the Yes column total: 30/(24+30) = 5/9.
SAT trap: Use the row or column total named by the condition.
TWO-WAY TABLES
MEDIUM
Question 21
A two-way table shows Group A has 20 Yes and 20 No responses, while Group B has 30 Yes and 20 No responses. What is P(No | Group B)?
Which choice is correct?
A) 2/9
B) 2/5
C) 1/2
D) 3/5
Show full solution
Correct answer: B) 2/5
Use the Group B row total: 20/(30+20) = 2/5.
SAT trap: Use the row or column total named by the condition.
TWO-WAY TABLES
MEDIUM
Question 22
A two-way table shows Group A has 35 Yes and 15 No responses, while Group B has 20 Yes and 30 No responses. What is P(Yes | Group A)?
Which choice is correct?
A) 7/20
B) 7/10
C) 3/10
D) 4/11
Show full solution
Correct answer: B) 7/10
Use the Group A row total: 35/(35+15) = 7/10.
SAT trap: Use the row or column total named by the condition.
TWO-WAY TABLES
MEDIUM
Question 23
A two-way table shows Group A has 42 Yes and 8 No responses, while Group B has 48 Yes and 12 No responses. What is P(Group B | Yes)?
Which choice is correct?
A) 21/55
B) 8/15
C) 4/25
D) 2/9
Show full solution
Correct answer: B) 8/15
Use the Yes column total: 48/(42+48) = 8/15.
SAT trap: Use the row or column total named by the condition.
TWO-WAY TABLES
MEDIUM
Question 24
A two-way table shows Group A has 26 Yes and 14 No responses, while Group B has 18 Yes and 22 No responses. What is P(No | Group B)?
Which choice is correct?
A) 13/40
B) 11/20
C) 7/20
D) 9/22
Show full solution
Correct answer: B) 11/20
Use the Group B row total: 22/(18+22) = 11/20.
SAT trap: Use the row or column total named by the condition.
TWO-WAY TABLES
MEDIUM
Question 25
A two-way table shows Group A has 30 Yes and 10 No responses, while Group B has 25 Yes and 15 No responses. What is P(Yes | Group A)?
Which choice is correct?
A) 3/8
B) 3/4
C) 1/4
D) 5/11
Show full solution
Correct answer: B) 3/4
Use the Group A row total: 30/(30+10) = 3/4.
SAT trap: Use the row or column total named by the condition.
TWO-WAY TABLES
MEDIUM
Question 26
A two-way table shows Group A has 36 Yes and 24 No responses, while Group B has 18 Yes and 22 No responses. What is P(Group B | Yes)?
Which choice is correct?
A) 9/25
B) 1/3
C) 2/5
D) 2/9
Show full solution
Correct answer: B) 1/3
Use the Yes column total: 18/(36+18) = 1/3.
SAT trap: Use the row or column total named by the condition.
TWO-WAY TABLES
MEDIUM
Question 27
A two-way table shows Group A has 27 Yes and 13 No responses, while Group B has 33 Yes and 17 No responses. What is P(No | Group B)?
Which choice is correct?
A) 3/10
B) 17/50
C) 13/40
D) 11/20
Show full solution
Correct answer: B) 17/50
Use the Group B row total: 17/(33+17) = 17/50.
SAT trap: Use the row or column total named by the condition.
TWO-WAY TABLES
MEDIUM
Question 28
A two-way table shows Group A has 40 Yes and 20 No responses, while Group B has 24 Yes and 16 No responses. What is P(Yes | Group A)?
Which choice is correct?
A) 2/5
B) 2/3
C) 1/3
D) 3/8
Show full solution
Correct answer: B) 2/3
Use the Group A row total: 40/(40+20) = 2/3.
SAT trap: Use the row or column total named by the condition.
TWO-WAY TABLES
MEDIUM
Question 29
A two-way table shows Group A has 15 Yes and 25 No responses, while Group B has 35 Yes and 25 No responses. What is P(Group B | Yes)?
Which choice is correct?
A) 3/20
B) 7/10
C) 5/8
D) 2/9
Show full solution
Correct answer: B) 7/10
Use the Yes column total: 35/(15+35) = 7/10.
SAT trap: Use the row or column total named by the condition.
TWO-WAY TABLES
MEDIUM
Question 30
A two-way table shows Group A has 48 Yes and 12 No responses, while Group B has 32 Yes and 8 No responses. What is P(No | Group B)?
Which choice is correct?
A) 12/25
B) 1/5
C) 2/5
D) 2/9
Show full solution
Correct answer: B) 1/5
Use the Group B row total: 8/(32+8) = 1/5.
SAT trap: Use the row or column total named by the condition.
How Do Dependent and Independent Events Differ?
Replacement determines whether the sample space changes.
DEPENDENT AND INDEPENDENT EVENTS
MEDIUM
Question 31
A bag contains 3 red and 2 blue marbles. One marble is drawn without replacement. Given that the first marble is red, what is the probability the second marble is red?
Which choice is correct?
A) 3/5
B) 1/2
C) 1/4
D) 2/5
Show full solution
Correct answer: B) 1/2
After applying the condition, 2 favorable marbles remain among 4 possible marbles. The probability is 1/2.
SAT trap: Replacement preserves the sample space; without replacement changes it.
DEPENDENT AND INDEPENDENT EVENTS
MEDIUM
Question 32
A bag contains 3 red and 2 blue marbles. One marble is drawn without replacement. Given that the first marble is blue, what is the probability the second marble is red?
Which choice is correct?
A) 3/5
B) 3/4
C) 1/2
D) 2/9
Show full solution
Correct answer: B) 3/4
After applying the condition, 3 favorable marbles remain among 4 possible marbles. The probability is 3/4.
SAT trap: Replacement preserves the sample space; without replacement changes it.
DEPENDENT AND INDEPENDENT EVENTS
MEDIUM
Question 33
A bag contains 4 red and 6 blue marbles. One marble is drawn and replaced. Given that the first marble is red, what is the probability the second marble is blue?
Which choice is correct?
A) 1/2
B) 3/5
C) 2/9
D) 3/10
Show full solution
Correct answer: B) 3/5
After applying the condition, 6 favorable marbles remain among 10 possible marbles. The probability is 3/5.
SAT trap: Replacement preserves the sample space; without replacement changes it.
DEPENDENT AND INDEPENDENT EVENTS
MEDIUM
Question 34
A bag contains 5 red and 5 blue marbles. One marble is drawn without replacement. Given that the first marble is red, what is the probability the second marble is blue?
Which choice is correct?
A) 1/2
B) 5/9
C) 4/9
D) 2/9
Show full solution
Correct answer: B) 5/9
After applying the condition, 5 favorable marbles remain among 9 possible marbles. The probability is 5/9.
SAT trap: Replacement preserves the sample space; without replacement changes it.
DEPENDENT AND INDEPENDENT EVENTS
MEDIUM
Question 35
A bag contains 6 red and 4 blue marbles. One marble is drawn without replacement. Given that the first marble is blue, what is the probability the second marble is blue?
Which choice is correct?
A) 2/5
B) 1/3
C) 2/9
D) 3/10
Show full solution
Correct answer: B) 1/3
After applying the condition, 3 favorable marbles remain among 9 possible marbles. The probability is 1/3.
SAT trap: Replacement preserves the sample space; without replacement changes it.
DEPENDENT AND INDEPENDENT EVENTS
MEDIUM
Question 36
A bag contains 7 red and 3 blue marbles. One marble is drawn and replaced. Given that the first marble is red, what is the probability the second marble is red?
Which choice is correct?
A) 3/5
B) 7/10
C) 2/9
D) 3/10
Show full solution
Correct answer: B) 7/10
After applying the condition, 7 favorable marbles remain among 10 possible marbles. The probability is 7/10.
SAT trap: Replacement preserves the sample space; without replacement changes it.
DEPENDENT AND INDEPENDENT EVENTS
MEDIUM
Question 37
A bag contains 2 red and 8 blue marbles. One marble is drawn without replacement. Given that the first marble is blue, what is the probability the second marble is red?
Which choice is correct?
A) 1/5
B) 2/9
C) 1/9
D) 3/10
Show full solution
Correct answer: B) 2/9
After applying the condition, 2 favorable marbles remain among 9 possible marbles. The probability is 2/9.
SAT trap: Replacement preserves the sample space; without replacement changes it.
DEPENDENT AND INDEPENDENT EVENTS
MEDIUM
Question 38
A bag contains 8 red and 2 blue marbles. One marble is drawn without replacement. Given that the first marble is red, what is the probability the second marble is blue?
Which choice is correct?
A) 1/5
B) 2/9
C) 1/9
D) 3/10
Show full solution
Correct answer: B) 2/9
After applying the condition, 2 favorable marbles remain among 9 possible marbles. The probability is 2/9.
SAT trap: Replacement preserves the sample space; without replacement changes it.
DEPENDENT AND INDEPENDENT EVENTS
MEDIUM
Question 39
A bag contains 5 red and 7 blue marbles. One marble is drawn and replaced. Given that the first marble is blue, what is the probability the second marble is blue?
Which choice is correct?
A) 1/2
B) 7/12
C) 2/9
D) 3/10
Show full solution
Correct answer: B) 7/12
After applying the condition, 7 favorable marbles remain among 12 possible marbles. The probability is 7/12.
SAT trap: Replacement preserves the sample space; without replacement changes it.
DEPENDENT AND INDEPENDENT EVENTS
MEDIUM
Question 40
A bag contains 9 red and 3 blue marbles. One marble is drawn without replacement. Given that the first marble is red, what is the probability the second marble is red?
Which choice is correct?
A) 3/4
B) 8/11
C) 7/11
D) 2/3
Show full solution
Correct answer: B) 8/11
After applying the condition, 8 favorable marbles remain among 11 possible marbles. The probability is 8/11.
SAT trap: Replacement preserves the sample space; without replacement changes it.
DEPENDENT AND INDEPENDENT EVENTS
MEDIUM
Question 41
A bag contains 4 red and 8 blue marbles. One marble is drawn without replacement. Given that the first marble is blue, what is the probability the second marble is red?
Which choice is correct?
A) 1/3
B) 4/11
C) 3/11
D) 2/9
Show full solution
Correct answer: B) 4/11
After applying the condition, 4 favorable marbles remain among 11 possible marbles. The probability is 4/11.
SAT trap: Replacement preserves the sample space; without replacement changes it.
DEPENDENT AND INDEPENDENT EVENTS
MEDIUM
Question 42
A bag contains 6 red and 6 blue marbles. One marble is drawn and replaced. Given that the first marble is red, what is the probability the second marble is blue?
Which choice is correct?
A) 5/12
B) 1/2
C) 2/9
D) 3/10
Show full solution
Correct answer: B) 1/2
After applying the condition, 6 favorable marbles remain among 12 possible marbles. The probability is 1/2.
SAT trap: Replacement preserves the sample space; without replacement changes it.
DEPENDENT AND INDEPENDENT EVENTS
MEDIUM
Question 43
A bag contains 10 red and 5 blue marbles. One marble is drawn without replacement. Given that the first marble is red, what is the probability the second marble is red?
Which choice is correct?
A) 2/3
B) 9/14
C) 4/7
D) 3/5
Show full solution
Correct answer: B) 9/14
After applying the condition, 9 favorable marbles remain among 14 possible marbles. The probability is 9/14.
SAT trap: Replacement preserves the sample space; without replacement changes it.
DEPENDENT AND INDEPENDENT EVENTS
MEDIUM
Question 44
A bag contains 3 red and 9 blue marbles. One marble is drawn without replacement. Given that the first marble is blue, what is the probability the second marble is blue?
Which choice is correct?
A) 3/4
B) 8/11
C) 7/11
D) 2/3
Show full solution
Correct answer: B) 8/11
After applying the condition, 8 favorable marbles remain among 11 possible marbles. The probability is 8/11.
SAT trap: Replacement preserves the sample space; without replacement changes it.
DEPENDENT AND INDEPENDENT EVENTS
MEDIUM
Question 45
A bag contains 7 red and 5 blue marbles. One marble is drawn and replaced. Given that the first marble is red, what is the probability the second marble is blue?
Which choice is correct?
A) 1/3
B) 5/12
C) 2/9
D) 3/10
Show full solution
Correct answer: B) 5/12
After applying the condition, 5 favorable marbles remain among 12 possible marbles. The probability is 5/12.
SAT trap: Replacement preserves the sample space; without replacement changes it.
Practice More SAT Data Analysis
Build accuracy with two-way tables and dependent events.
How Are Complements and Reverse Conditions Tested?
Translate the notation before calculating.
COMPLEMENTS AND REVERSE CONDITIONS
MEDIUM
Question 46
If P(A and B)=0.24 and P(B)=0.60, what is P(A | B)?
Which choice is correct?
A) 1/5
B) 2/5
C) 4/5
D) 3/5
Show full solution
Correct answer: B) 2/5
Compute 0.24/0.60 = 0.40.
SAT trap: Translate the notation before choosing the operation.
COMPLEMENTS AND REVERSE CONDITIONS
HARD
Question 47
If P(A | B)=0.30 and P(B)=0.50, what is P(A and B)?
Which choice is correct?
A) 3/40
B) 3/20
C) 3/10
D) 17/20
Show full solution
Correct answer: B) 3/20
Multiply 0.30 by 0.50.
SAT trap: Translate the notation before choosing the operation.
COMPLEMENTS AND REVERSE CONDITIONS
MEDIUM
Question 48
If P(A | B)=0.70, what is P(not A | B)?
Which choice is correct?
A) 3/20
B) 3/10
C) 3/5
D) 7/10
Show full solution
Correct answer: B) 3/10
Take the complement: 1-0.70.
SAT trap: Translate the notation before choosing the operation.
COMPLEMENTS AND REVERSE CONDITIONS
MEDIUM
Question 49
If P(A)=0.40 and A and B are independent, what is P(A | B)?
Which choice is correct?
A) 1/5
B) 2/5
C) 4/5
D) 3/5
Show full solution
Correct answer: B) 2/5
For independent events, P(A | B)=P(A).
SAT trap: Translate the notation before choosing the operation.
COMPLEMENTS AND REVERSE CONDITIONS
MEDIUM
Question 50
If P(A)=0.70, P(B)=0.50, and P(A and B)=0.35, what is P(A | B)?
Which choice is correct?
A) 7/20
B) 7/10
C) 1
D) 3/10
Show full solution
Correct answer: B) 7/10
Compute 0.35/0.50.
SAT trap: Translate the notation before choosing the operation.
COMPLEMENTS AND REVERSE CONDITIONS
HARD
Question 51
If P(A or B)=0.80, P(A)=0.50, and P(B)=0.60, what is P(A and B)?
Which choice is correct?
A) 3/20
B) 3/10
C) 3/5
D) 7/10
Show full solution
Correct answer: B) 3/10
Use P(A or B)=P(A)+P(B)-P(A and B).
SAT trap: Translate the notation before choosing the operation.
COMPLEMENTS AND REVERSE CONDITIONS
MEDIUM
Question 52
If P(A and B)=0 and P(B)>0, what is P(A | B)?
Which choice is correct?
A) 1
B) 0
C) 2/9
D) 3/10
Show full solution
Correct answer: B) 0
The events never occur together.
SAT trap: Translate the notation before choosing the operation.
COMPLEMENTS AND REVERSE CONDITIONS
HARD
Question 53
If P(A and B)=0.18 and P(A)=0.45, what is P(B | A)?
Which choice is correct?
A) 1/5
B) 2/5
C) 4/5
D) 3/5
Show full solution
Correct answer: B) 2/5
Compute 0.18/0.45.
SAT trap: Translate the notation before choosing the operation.
COMPLEMENTS AND REVERSE CONDITIONS
MEDIUM
Question 54
If P(A | B)=P(A), what numerical factor describes the unchanged relationship?
Which choice is correct?
A) 1/2
B) 1
C) 0
D) 2/9
Show full solution
Correct answer: B) 1
The conditional probability equals the original probability, indicating independence.
SAT trap: Translate the notation before choosing the operation.
COMPLEMENTS AND REVERSE CONDITIONS
HARD
Question 55
A group is 25% of a population, and 60% of that group satisfies X. What fraction of the population is in the group and satisfies X?
Which choice is correct?
A) 3/40
B) 3/20
C) 3/10
D) 17/20
Show full solution
Correct answer: B) 3/20
Multiply 0.25 by 0.60.
SAT trap: Translate the notation before choosing the operation.
What Do Hard Mixed Questions Look Like?
These questions combine weighted groups and restricted outcomes.
HARD MIXED CONDITIONAL PROBABILITY
HARD
Question 56
Group A is 60% of a population and Group B is 40%. Condition X occurs in 40% of Group A and 30% of Group B. Given that a person has X, what is the probability the person is from Group A?
Which choice is correct?
A) 6/25
B) 2/3
C) 3/5
D) 1/3
Show full solution
Correct answer: B) 2/3
Group A contributes 24.0% and Group B contributes 12.0% of the population with X. Therefore the probability is 2/3.
SAT trap: Weight each conditional rate by its group proportion before reversing the condition.
HARD MIXED CONDITIONAL PROBABILITY
HARD
Question 57
Group A is 70% of a population and Group B is 30%. Condition X occurs in 20% of Group A and 50% of Group B. Given that a person has X, what is the probability the person is from Group A?
Which choice is correct?
A) 7/50
B) 14/29
C) 7/10
D) 15/29
Show full solution
Correct answer: B) 14/29
Group A contributes 14.0% and Group B contributes 15.0% of the population with X. Therefore the probability is 14/29.
SAT trap: Weight each conditional rate by its group proportion before reversing the condition.
HARD MIXED CONDITIONAL PROBABILITY
HARD
Question 58
Group A is 55% of a population and Group B is 45%. Condition X occurs in 60% of Group A and 20% of Group B. Given that a person has X, what is the probability the person is from Group A?
Which choice is correct?
A) 33/100
B) 11/14
C) 11/20
D) 3/14
Show full solution
Correct answer: B) 11/14
Group A contributes 33.0% and Group B contributes 9.0% of the population with X. Therefore the probability is 11/14.
SAT trap: Weight each conditional rate by its group proportion before reversing the condition.
HARD MIXED CONDITIONAL PROBABILITY
HARD
Question 59
Group A is 80% of a population and Group B is 20%. Condition X occurs in 10% of Group A and 40% of Group B. Given that a person has X, what is the probability the person is from Group A?
Which choice is correct?
A) 2/25
B) 1/2
C) 4/5
D) 2/9
Show full solution
Correct answer: B) 1/2
Group A contributes 8.0% and Group B contributes 8.0% of the population with X. Therefore the probability is 1/2.
SAT trap: Weight each conditional rate by its group proportion before reversing the condition.
HARD MIXED CONDITIONAL PROBABILITY
HARD
Question 60
Group A is 65% of a population and Group B is 35%. Condition X occurs in 30% of Group A and 50% of Group B. Given that a person has X, what is the probability the person is from Group A?
Which choice is correct?
A) 39/200
B) 39/74
C) 13/20
D) 35/74
Show full solution
Correct answer: B) 39/74
Group A contributes 19.5% and Group B contributes 17.5% of the population with X. Therefore the probability is 39/74.
SAT trap: Weight each conditional rate by its group proportion before reversing the condition.
HARD MIXED CONDITIONAL PROBABILITY
HARD
Question 61
Two fair dice are rolled. Given that the sum is 8, what is the probability one die shows 3?
Which choice is correct?
A) 1/5
B) 2/5
C) 4/5
D) 3/5
Show full solution
Correct answer: B) 2/5
Five ordered outcomes sum to 8, and two contain a 3.
SAT trap: List only outcomes satisfying the condition.
HARD MIXED CONDITIONAL PROBABILITY
HARD
Question 62
Two fair dice are rolled. Given that at least one die shows 6, what is the probability the sum is 9?
Which choice is correct?
A) 1/11
B) 2/11
C) 4/11
D) 9/11
Show full solution
Correct answer: B) 2/11
There are 11 ordered outcomes with at least one 6, and two sum to 9.
SAT trap: List only outcomes satisfying the condition.
HARD MIXED CONDITIONAL PROBABILITY
HARD
Question 63
A bag has 4 red and 6 blue marbles. Two are drawn without replacement. Given that at least one is red, what is the probability both are red?
Which choice is correct?
A) 1/10
B) 1/5
C) 2/5
D) 4/5
Show full solution
Correct answer: B) 1/5
Divide P(both red)=6/45 by P(at least one red)=30/45.
SAT trap: List only outcomes satisfying the condition.
HARD MIXED CONDITIONAL PROBABILITY
HARD
Question 64
A card is selected from a standard deck. Given that it is a face card, what is the probability it is a king?
Which choice is correct?
A) 1/6
B) 1/3
C) 2/3
D) 2/9
Show full solution
Correct answer: B) 1/3
There are 12 face cards and 4 kings.
SAT trap: List only outcomes satisfying the condition.
HARD MIXED CONDITIONAL PROBABILITY
HARD
Question 65
A number is selected from 1 through 30. Given that it is divisible by 3, what is the probability it is divisible by 6?
Which choice is correct?
A) 1/4
B) 1/2
C) 1
D) 2/9
Show full solution
Correct answer: B) 1/2
There are 10 multiples of 3 and 5 are multiples of 6.
SAT trap: List only outcomes satisfying the condition.
What Do Student-Produced Responses Look Like?
Enter the requested fraction or decimal.
STUDENT-PRODUCED RESPONSE
MEDIUM
Question 66
Of 40 chess players, 30 also play tennis. What is P(tennis | chess)?
Enter your answer.
Show full solution
Correct answer: 3/4
Use 30/40.
SAT trap: Enter the simplified fraction or equivalent decimal.
STUDENT-PRODUCED RESPONSE
MEDIUM
Question 67
A number is chosen from 1 through 18. Given that it is even, what is the probability it is divisible by 6?
Enter your answer.
Show full solution
Correct answer: 1/3
There are 9 even numbers and 3 are divisible by 6.
SAT trap: Enter the simplified fraction or equivalent decimal.
STUDENT-PRODUCED RESPONSE
MEDIUM
Question 68
If P(A and B)=0.18 and P(B)=0.60, what is P(A | B)?
Enter your answer.
Show full solution
Correct answer: 3/10
Compute 0.18/0.60.
SAT trap: Enter the simplified fraction or equivalent decimal.
STUDENT-PRODUCED RESPONSE
MEDIUM
Question 69
A bag has 5 red and 5 blue marbles. Without replacement, given that the first is red, what is P(second is blue)?
Enter your answer.
Show full solution
Correct answer: 5/9
Five blue marbles remain among 9 total.
SAT trap: Enter the simplified fraction or equivalent decimal.
STUDENT-PRODUCED RESPONSE
MEDIUM
Question 70
Among 30 dog owners, 18 also own a cat. What is P(cat | dog)?
Enter your answer.
Show full solution
Correct answer: 3/5
Compute 18/30.
SAT trap: Enter the simplified fraction or equivalent decimal.
Common Mistakes
| Mistake | Correction |
|---|---|
| Using the grand total | Use the conditioned total |
| Reversing P(A|B) | Translate it into words |
| Ignoring replacement | Update the sample space |
Two-Week Study Plan
| Days | Focus |
|---|---|
| 1-3 | Q1-Q15 |
| 4-7 | Q16-Q30 |
| 8-10 | Q31-Q45 |
| 11-14 | Q46-Q70 and review |
Frequently Asked Questions
Are conditional probability questions on the Digital SAT?
Yes. They often appear with surveys, tables, and dependent events.
What does P(A | B) mean?
The probability of A given B.
What is the formula?
P(A | B)=P(A and B)/P(B).
How do I choose the denominator?
Use the total satisfying the condition after the vertical bar.
Are P(A | B) and P(B | A) equal?
Not usually.
How does replacement matter?
Without replacement, probabilities usually change.
How can I test independence?
Check whether P(A | B)=P(A).
How many questions should I practice?
Practice across direct, table, dependent, and reverse-condition models.
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