Conditional Probability Review

In a factory, two machines produce items. Machine A produces 60% of the items, and 3% of its items are defective. Machine B produces 40% of the items, and 5% of its items are defective. If a randomly selected item is defective, what is the probability that it was produced by Machine A?

• 0.26

• 0.36

• 0.45

• 0.54

A survey shows that 70% of people who own a smartphone also own a tablet. It also shows that 40% of all people own a smartphone. What is the probability that a randomly selected person owns a tablet given that they own a smartphone?

• 0.28

• 0.40

• 0.57

• 0.70

A weather forecast predicts a 70% chance of rain on Saturday and an 80% chance of rain on Sunday. The probability of rain on both days is 60%. What is the probability of rain on Sunday given that it rained on Saturday?

• 0.42

• 0.60

• 0.75

• 0.86

In a high school, 40% of students play a sport. Of the students who play a sport, 30% are on the football team. What is the probability that a randomly selected student who plays a sport is on the football team?

• 0.12

• 0.30

• 0.40

• 0.70

A company finds that 60% of its employees take the bus to work. Of those who take the bus, 75% live within 5 miles of the office. What is the probability that a randomly selected employee who takes the bus lives within 5 miles of the office?

• 0.45

• 0.60

• 0.75

• 0.90

A store sells two brands of light bulbs, Brand X and Brand Y. 80% of bulbs sold are Brand X, and 20% are Brand Y. 1% of Brand X bulbs are defective, and 3% of Brand Y bulbs are defective. If a randomly purchased bulb is defective, what is the probability that it is Brand Y?

• 0.006 / 0.014

• 0.006 / 0.008

• 0.024 / 0.014

• 0.024 / 0.008

A study shows that 90% of people who have a certain disease test positive for it. Also, 5% of people who do not have the disease also test positive (false positive). If 2% of the population has the disease, what is the probability that a person who tests positive actually has the disease?

• (0.90 * 0.02) / [(0.90 * 0.02) + (0.05 * 0.98)]

• (0.90 * 0.02) / (0.05 * 0.98)

• (0.05 * 0.98) / [(0.90 * 0.02) + (0.05 * 0.98)]

• (0.90 * 0.02) / 0.02

At a university, 70% of students are undergraduates, and 30% are graduate students. 60% of undergraduates live on campus, and 80% of graduate students live on campus. If a randomly selected student lives on campus, what is the probability that they are a graduate student?

• (0.30 * 0.80) / [(0.70 * 0.60) + (0.30 * 0.80)]

• (0.70 * 0.60) / [(0.70 * 0.60) + (0.30 * 0.80)]

• (0.30 * 0.80) / (0.70 * 0.60)

• (0.70 * 0.60) / (0.30 * 0.80)

A car manufacturer knows that 5% of the cars they produce have a defect in the engine, and 2% have a defect in the transmission. 0.5% of cars have both defects. What is the probability that a car with a transmission defect also has an engine defect?

• 0.005 / 0.02

• 0.02 / 0.005

• 0.05 / 0.02

• 0.02 / 0.05

In a survey, 80% of people said they like chocolate. Of those who like chocolate, 60% also like vanilla. What is the probability that a randomly selected person who likes chocolate also likes vanilla?

• 0.48

• 0.60

• 0.75

• 0.80