Probability and Conditional Probability Flashcards

A factory produces light bulbs; 2% are defective. If a quality checker tests 3 bulbs independently, what is the probability that none are defective?

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.

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?

Answer: 0.0588

P(at least one defective) = 1 − (0.98)³ = 1 − 0.9412 ≈ 0.0588.

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?

Answer: 2/5

Total satisfied = 60 + 90 = 150; public transit & satisfied = 60; P = 60/150 = 2/5.

Events A and B are independent. P(A) = 0.4 and P(B) = 0.3. What is P(A and B)?

Answer: 0.12

For independent events, P(A and B) = P(A) × P(B) = 0.4 × 0.3 = 0.12.

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?

Answer: 3/10

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

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?

Answer: 2/5

P(tablet | smartphone) = P(both)/P(smartphone) = 36/90 = 2/5.

A game has a 1/4 probability of winning each round. What is the probability of winning at least once in 2 independent rounds?

Answer: 7/16

P(at least one win) = 1 − P(no wins) = 1 − (3/4)² = 1 − 9/16 = 7/16.