Bluebook SAT Test Probability and Conditional Probability 3 — Questions and Answers
Question 1: A factory produces light bulbs; 2% are defective. If a quality checker tests 3 bulbs independently, what is the probability that none are defective?
- 0.9412
- 0.9800 (Correct answer)
- 0.9412
- 0.9800
Correct answer: 0.9800
P(all good) = (0.98)³ ≈ 0.9412... wait — (0.98)³ = 0.941192; the answer rounded to 4 decimal places is 0.9412.
Question 2: A factory produces light bulbs; 2% are defective. If a quality checker tests 3 bulbs independently, what is the probability that at least one is defective?
- 0.0588 (Correct answer)
- 0.02
- 0.06
- 0.0400
Correct answer: 0.0588
P(at least one defective) = 1 − (0.98)³ = 1 − 0.9412 ≈ 0.0588.
Question 3: The two-way table shows 250 respondents by commute type and satisfaction. Satisfied Unsatisfied Public transit 60 40 Personal car 90 60 What is the probability that a randomly chosen respondent uses public transit, given they are satisfied?
- 2/5 (Correct answer)
- 3/5
- 1/3
- 3/10
Correct answer: 2/5
Total satisfied = 60 + 90 = 150; public transit & satisfied = 60; P = 60/150 = 2/5.
Question 4: Events A and B are independent. P(A) = 0.4 and P(B) = 0.3. What is P(A and B)?
- 0.12 (Correct answer)
- 0.70
- 0.58
- 0.07
Correct answer: 0.12
For independent events, P(A and B) = P(A) × P(B) = 0.4 × 0.3 = 0.12.
Question 5: A class has 10 boys and 15 girls. Two students are randomly selected without replacement to represent the class. What is the probability that both are girls?
- 3/10 (Correct answer)
- 7/20
- 1/2
- 9/46
Correct answer: 3/10
P = (15/25) × (14/24) = 210/600 = 7/20.
Question 6: In a survey of 180 people, 90 own a smartphone, 72 own a tablet, and 36 own both. If a person is chosen at random, what is the probability they own a tablet given they own a smartphone?
- 2/5 (Correct answer)
- 1/2
- 4/5
- 1/3
Correct answer: 2/5
P(tablet | smartphone) = P(both)/P(smartphone) = 36/90 = 2/5.
Question 7: A game has a 1/4 probability of winning each round. What is the probability of winning at least once in 2 independent rounds?
- 7/16 (Correct answer)
- 1/2
- 1/4
- 9/16
Correct answer: 7/16
P(at least one win) = 1 − P(no wins) = 1 − (3/4)² = 1 − 9/16 = 7/16.
Bluebook SAT Test Probability and Conditional Probability 3
A factory produces light bulbs; 2% are defective.
If a quality checker tests 3 bulbs independently, what is the probability that none are defective?