Probability and Conditional Probability Flashcards

A spinner has 8 equal sections numbered 1–8. What is the probability of landing on a prime number?

Answer: 1/2

Primes from 1–8 are 2, 3, 5, 7 — that's 4 values, so P = 4/8 = 1/2.

Of 500 adults surveyed, 300 exercise regularly and 200 do not. Among those who exercise, 240 reported good health; among those who don't, 60 reported good health. What is the probability that a randomly selected adult who reports good health exercises regularly?

Answer: 4/5

Total reporting good health = 240 + 60 = 300; exercisers = 240, so P = 240/300 = 4/5.

A box contains 5 defective and 15 non-defective items. Two items are selected at random without replacement. What is the probability that the first is defective and the second is non-defective?

Answer: 15/76

P(1st defective) = 5/20; P(2nd non-defective | 1st defective) = 15/19; product = 75/380 = 15/76.

In a group of 80 people, 50 drink coffee and 40 drink tea. If the probability of drinking both is 0.25, how many people drink coffee or tea?

Answer: 70

P(both) = 0.25 means 20 people; P(coffee or tea) count = 50 + 40 − 20 = 70.

The two-way table shows 400 students categorized by grade and club membership. In Club Not in Club Grade 9-10 80 120 Grade 11-12 100 100 A student is chosen at random. What is the probability the student is in a club, given they are in Grade 11–12?

Answer: 1/2

Grade 11–12 total = 100 + 100 = 200; in club = 100, so P = 100/200 = 1/2.

A coin is flipped 3 times. What is the probability of getting exactly 2 heads?

Answer: 3/8

C(3,2) = 3 favorable outcomes out of 2³ = 8 total; P = 3/8.

A card is drawn from a standard 52-card deck. What is the probability it is a heart OR a king?

Answer: 4/13

Hearts = 13, kings = 4, king of hearts counted twice: 13 + 4 − 1 = 16; P = 16/52 = 4/13.