Probability and Conditional Probability Flashcards

A fair six-sided die is rolled once. What is the probability of rolling a number greater than 4?

Answer: 1/3

Numbers greater than 4 are 5 and 6 — that's 2 out of 6, which equals 1/3.

A survey of 300 adults found that 180 own a car, 120 own a bike, and 60 own both. What is the probability a randomly selected adult owns a car but NOT a bike?

Answer: 1/3

Car only = 180 − 60 = 120; P = 120/300 = 2/5.

A factory has two machines. Machine 1 produces 60% of items; Machine 2 produces 40%. Machine 1 has a 5% defect rate; Machine 2 has a 10% defect rate. What percent of all items are defective?

Answer: 7%

0.60(0.05) + 0.40(0.10) = 0.03 + 0.04 = 0.07 = 7%.

Two cards are drawn from a 52-card deck without replacement. What is the probability both are aces?

Answer: 1/221

P = (4/52)(3/51) = 12/2652 = 1/221.

The two-way table shows 240 students by grade and preferred study location. Library Home Grade 11 60 80 Grade 12 40 60 Given a student is in Grade 12, what is the probability they prefer the Library?

Answer: 2/5

Grade 12 total = 40 + 60 = 100; P(Library | Grade 12) = 40/100 = 2/5.

A bag contains 4 red and 6 blue tokens. One token is drawn, its color noted, and it is returned. This is repeated a second time. What is the probability of drawing a different color each time?

Answer: 12/25

P(R then B) + P(B then R) = (4/10)(6/10) + (6/10)(4/10) = 24/100 + 24/100 = 48/100 = 12/25.

In a group of 50 athletes, 30 play basketball and 25 play soccer. If 10 play both sports, what is the probability a randomly chosen athlete plays at least one sport?

Answer: 9/10

At least one = 30 + 25 − 10 = 45; P = 45/50 = 9/10.