Bluebook SAT Test Probability and Conditional Probability — Questions and Answers

Question 1: A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If one marble is drawn at random, what is the probability that it is NOT green?

1/5
4/5 (Correct answer)
2/5
3/5

Correct answer: 4/5

There are 8 non-green marbles out of 10 total, so P(not green) = 8/10 = 4/5.

Question 2: A survey of 200 students found that 120 play sports and 80 play an instrument. If 40 students do both, how many students do neither?

40 (Correct answer)
80
120
160

Correct answer: 40

Using inclusion-exclusion: sports or instrument = 120 + 80 − 40 = 160, so neither = 200 − 160 = 40.

Question 3: The two-way table shows pet ownership among 150 households. Cat No Cat Dog 30 45 No Dog 25 50 Given that a household has a dog, what is the probability it also has a cat?

2/5 (Correct answer)
2/3
1/5
3/10

Correct answer: 2/5

There are 30 + 45 = 75 dog households; 30 have both, so P(cat | dog) = 30/75 = 2/5.

Question 4: A standard die is rolled twice. What is the probability of getting a 4 on the first roll and a number greater than 2 on the second roll?

1/9 (Correct answer)
1/6
2/9
1/3

Correct answer: 1/9

P(4) = 1/6 and P(>2) = 4/6 = 2/3; since independent, multiply: (1/6)(2/3) = 2/18 = 1/9.

Question 5: In a class of 30 students, 18 passed the math test and 12 passed the science test. If 6 students passed both, what is the probability that a randomly selected student passed at least one test?

4/5 (Correct answer)
3/5
2/3
1/2

Correct answer: 4/5

Students passing at least one = 18 + 12 − 6 = 24; P = 24/30 = 4/5.

Question 6: A jar has 4 red and 6 blue chips. Two chips are drawn without replacement. What is the probability that both chips are red?

2/15 (Correct answer)
4/25
8/25
1/5

Correct answer: 2/15

P(1st red) = 4/10; P(2nd red | 1st red) = 3/9; product = 12/90 = 2/15.

Question 7: The table below shows 300 survey responses by age group and preference. Prefer A Prefer B Under 30 90 60 30 and over 80 70 What is the probability that a randomly chosen respondent under 30 prefers A?

3/5 (Correct answer)
9/25
9/20
3/10

Correct answer: 3/5

There are 90 + 60 = 150 respondents under 30; 90 prefer A, so P = 90/150 = 3/5.

Question 8: A two-way table records 400 employees by department and satisfaction level. Satisfied Neutral Dissatisfied Engineering 80 40 30 Marketing 60 60 50 Operations 40 20 20 What is the probability a randomly selected employee is from Marketing and Dissatisfied?

1/8 (Correct answer)
5/40
1/10
1/4

Correct answer: 1/8

Marketing & Dissatisfied = 50 out of 400 total; P = 50/400 = 1/8.

Question 9: P(A) = 0.6 and P(A and B) = 0.18. If A and B are independent, what is P(B)?

0.30 (Correct answer)
0.18
0.42
0.78

Correct answer: 0.30

Since A and B are independent, P(B) = P(A and B)/P(A) = 0.18/0.6 = 0.30.

Question 10: A box has 3 red, 5 white, and 2 black balls. One ball is drawn and not replaced; then a second is drawn. What is the probability the second ball is red, given the first was white?

1/3 (Correct answer)
3/10
3/9
1/4

Correct answer: 1/3

After removing a white ball, 9 balls remain: 3 red; P = 3/9 = 1/3.

Question 11: A game wheel has 4 red, 3 blue, and 1 green section. A player spins twice. What is the probability of getting green both times?

1/64 (Correct answer)
1/8
1/16
3/64

Correct answer: 1/64

P(green) = 1/8; for two independent spins, P = (1/8)² = 1/64.

Question 12: In a class of 25 students, the probability that a randomly chosen student plays guitar is 0.32. What is the expected number of guitar players?

8 (Correct answer)
7
6
10

Correct answer: 8

Expected value = 25 × 0.32 = 8.

Question 13: The two-way table shows 500 people by exercise frequency and BMI category. Normal BMI High BMI Exercise daily 180 70 Rarely exercise 90 160 What fraction of people with a Normal BMI exercise daily?

2/3 (Correct answer)
9/10
3/5
18/27

Correct answer: 2/3

Normal BMI total = 180 + 90 = 270; exercise daily = 180; P = 180/270 = 2/3.

Question 14: A bag has 7 green and 3 yellow tokens. Two tokens are drawn with replacement. What is the probability of drawing one of each color?

42/100 (Correct answer)
21/50
3/10
49/100

Correct answer: 42/100

P(green then yellow) + P(yellow then green) = (7/10)(3/10) + (3/10)(7/10) = 42/100 = 21/50.

Question 15: A class has 24 students. The probability of any student being absent on a given day is 0.05. What is the expected number of absent students?

1.2 (Correct answer)
1.0
0.5
2.4

Correct answer: 1.2

E = n × p = 24 × 0.05 = 1.2.

Question 16: The two-way table shows 200 voters by party and stance on a bill. Favor Oppose Democrat 70 30 Republican 20 80 Given that a voter favors the bill, what is the probability the voter is a Republican?

2/9 (Correct answer)
1/5
4/9
2/11

Correct answer: 2/9

Total favoring = 70 + 20 = 90; Republicans favoring = 20; P = 20/90 = 2/9.

Question 17: Cards numbered 1 through 20 are shuffled. One card is drawn at random. What is the probability the card shows a multiple of 3 or a multiple of 5?

2/5 (Correct answer)
1/2
9/20
7/20

Correct answer: 2/5

Multiples of 3: {3,6,9,12,15,18} = 6; multiples of 5: {5,10,15,20} = 4; overlap {15} = 1; union = 9; P = 9/20.

Question 18: A bag has 5 red and 5 blue chips. Two chips are drawn without replacement. What is the probability both are the same color?

4/9 (Correct answer)
1/2
2/5
5/9

Correct answer: 4/9

P(RR) = (5/10)(4/9) = 20/90; P(BB) = (5/10)(4/9) = 20/90; total = 40/90 = 4/9.

Question 19: A company's hiring data shows: 40% of applicants pass the written test and, of those, 30% pass the interview. What percent of all applicants get hired?

12% (Correct answer)
30%
40%
70%

Correct answer: 12%

P(pass written and interview) = 0.40 × 0.30 = 0.12 = 12%.

Question 20: The two-way table shows 300 students by study method and test result. Pass Fail Study group 110 40 Study alone 90 60 What is the probability a student who failed studied alone?

3/5 (Correct answer)
1/3
2/5
3/10

Correct answer: 3/5

Total failing = 40 + 60 = 100; studied alone and failed = 60; P = 60/100 = 3/5.

Question 21: A number is selected at random from 1 to 50. What is the probability it is divisible by both 4 and 6?

2/25 (Correct answer)
1/10
1/12
3/50

Correct answer: 2/25

LCM(4,6) = 12; multiples of 12 up to 50: {12, 24, 36, 48} = 4; P = 4/50 = 2/25.

Bluebook SAT Test Probability and Conditional Probability

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles.
If one marble is drawn at random, what is the probability that it is NOT green?

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