Bluebook SAT Test Probability and Conditional Probability 1 — 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.
Bluebook SAT Test Probability and Conditional Probability 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?