Bluebook SAT Test Probability and Conditional Probability 14

Question 1

A bucket has 6 tennis balls and 4 golf balls. Two balls are drawn at random with replacement. What is the probability both are golf balls?

Accepted Answer

4/25

Answer

P = (4/10)(4/10) = 16/100 = 4/25.

Question 2

The two-way table shows 320 people by diet type and cholesterol level.

High Cholesterol   Normal
Plant-based               30          90
Omnivore                  80         120

Given a person has high cholesterol, what is the probability they follow a plant-based diet?

Accepted Answer

3/11

Answer

High cholesterol total = 30 + 80 = 110; P(plant-based | high chol) = 30/110 = 3/11.

Question 3

Of 60 light bulbs in stock, 12 are defective. If 2 are selected at random without replacement, what is the probability neither is defective?

Accepted Answer

188/295

Answer

P = (48/60)(47/59) = 2256/3540 = 188/295.

Question 4

P(A | B) = 0.4 and P(B) = 0.25. What is P(A and B)?

Accepted Answer

0.10

Answer

P(A and B) = P(A | B) × P(B) = 0.4 × 0.25 = 0.10.

Question 5

A poll shows that 70% of voters in a city support Policy X. If 3 voters are chosen independently, what is the probability all 3 support Policy X?

Accepted Answer

0.343

Answer

(0.70)^3 = 0.343.

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