Bluebook SAT Test Probability and Conditional Probability 3

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?

Accepted Answer

0.9800

Answer

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?

Accepted Answer

0.0588

Answer

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?

Accepted Answer

2/5

Answer

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)?

Accepted Answer

0.12

Answer

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?

Accepted Answer

3/10

Answer

P = (15/25) × (14/24) = 210/600 = 7/20.

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test Probability and Conditional Probability 3