Mastering Conditional Probability and Bayes' Theorem

A factory produces light bulbs, 90% of which pass quality control. If 80% of the bulbs that pass are from Machine A, what is the probability that a bulb from Machine A passes quality control?

• 72%

• 90%

• 85%

• 60%

In a school, 60% of students are girls. If 70% of the girls and 50% of the boys passed the math exam, what is the probability that a student who passed the exam is a girl?

• 25/31

• 15/31

• 21/31

• 30/31

A medical test for a disease is 95% accurate. If 1% of the population has the disease, what is the probability that a person who tests positive actually has the disease?

• 50%

• Approximately 16.1%

• 5%

• 90%

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

• 1/3

• 2/3

• 1/2

• 1/4

A survey shows that 40% of people prefer coffee over tea. If 30% of coffee drinkers are under 30 years old, what is the probability that a randomly selected coffee drinker is under 30?

• 0.50

• 0.30

• 0.20

• 0.40

In a city, 20% of the population are smokers. If 10% of smokers develop lung cancer, what is the probability that a randomly selected person with lung cancer is a smoker?

• 10%

• 20%

• 50%

• 30%

A bag contains 5 red and 3 blue marbles. If a marble is drawn and it is red, what is the probability that the next marble drawn is also red?

• 5/8

• 1/2

• 3/7

• 4/7

In a tech company, 70% of employees are engineers. If 90% of engineers have a degree, what is the probability that a randomly selected employee with a degree is an engineer?

• 75%

• 50%

• 67.74%

• 80%

A restaurant finds that 80% of its customers are satisfied. If 50% of satisfied customers return, what is the probability that a customer who returns was satisfied?

• 0.2

• 0.8

• 0.5

• 1.0

In a game, the probability of winning is 0.2. If a player wins, the probability of receiving a bonus is 0.5. What is the probability that a player receives a bonus?

• 0.3

• 0.2

• 0.05

• 0.1