Probability and Conditional Probability Flashcards

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?

Answer: 4/25

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

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?

Answer: 3/11

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

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

Answer: 188/295

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

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

Answer: 0.10

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

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?

Answer: 0.343

(0.70)^3 = 0.343.

A class of 30 students has 12 athletes and 18 non-athletes. 8 of the athletes have part-time jobs; 6 of the non-athletes have part-time jobs. If a student with a part-time job is chosen at random, what is the probability the student is an athlete?

Answer: 4/7

Total with jobs = 8 + 6 = 14; P(athlete | job) = 8/14 = 4/7.

A number is selected at random from integers 1–25. What is the probability the number is prime?

Answer: 9/25

Primes in 1–25: 2,3,5,7,11,13,17,19,23 — that's 9; P = 9/25.