Mastering Conditional Probability and Bayes' Theorem

A bag contains 3 red balls and 2 blue balls. If a ball is drawn at random, what is the probability that it is red given that it is not blue?

• 0.5

• 2

• 3

• 1

In a school, 60% of students are girls. If a student is selected at random and is known to be a girl, what is the probability that she is in the honors program if 30% of girls are in honors?

• 0.6

• 0.1

• 0.3

• 0.5

A factory produces 80% of its products without defects. If a defective product is found, what is the probability that it came from machine A, given that machine A produces 70% of the total products?

• 50%

• 80%

• 60%

• 70%

In a survey, 40% of people prefer coffee over tea. If a person is known to prefer coffee, what is the probability that they also drink tea, given that 25% of coffee drinkers also drink tea?

• 50%

• 10%

• 25%

• 75%

A medical test for a disease is 90% accurate. If 1% of the population has the disease, what is the probability that a person has the disease given that they tested positive?

• 50%

• 15%

• 5%

• 8.33%

In a deck of cards, what is the probability of drawing a heart given that the card drawn is a face card?

• 1/4

• 2/5

• 1/3

• 1/2

A company has two types of products: A and B. Product A has a 95% success rate, while product B has a 70% success rate. If a product is chosen at random and is successful, what is the probability that it is product A?

• 0.45

• 0.80

• 0.576

• 0.65

In a city, 70% of the population owns a car. If a person is known to own a car, what is the probability that they also own a motorcycle, given that 20% of car owners also own a motorcycle?

• 0.5

• 0.8

• 0.2

• 0.1

A student takes two subjects: Math and Science. If 40% of students pass Math and 50% pass Science, and 20% pass both, what is the probability that a student passes Math given that they passed Science?

• 50%

• 30%

• 40%

• 20%

In a game, the probability of winning is 0.4. If a player wins, what is the probability that they will play again, given that 60% of winners choose to play again?

• 0.5

• 0.2

• 0.8

• 0.6