Conditional Probability: Venn Diagrams in Real Scenarios

A school has 200 students, 120 of whom play soccer and 80 play basketball. If a student is chosen at random, what is the probability that they play basketball given that they play soccer?

• x / 120, where x is the number of students who play both soccer and basketball.

• x / 200, where x is the number of students who play soccer only.

• x / 120, where x is the total number of students in the school.

• x / 80, where x is the number of students who play both soccer and basketball.

In a survey, 60% of people prefer coffee, and 30% of those who prefer coffee also prefer tea. What is the probability that a randomly selected person prefers tea given that they prefer coffee?

• 20%

• 50%

• 40%

• 30%

A company found that 70% of its employees are satisfied with their jobs. Among those satisfied, 40% are also likely to recommend the company to others. What is the probability that an employee will recommend the company given that they are satisfied?

• 0.4

• 0.7

• 0.2

• 0.5

In a class of 30 students, 18 are girls and 12 are boys. If a student is selected at random, what is the probability that the student is a boy given that the student is not a girl?

• 3

• 1

• 0.5

• 2

A restaurant offers two types of desserts: cakes and ice creams. 40% of customers order cakes, and 25% of those who order cakes also order coffee. What is the probability that a customer orders coffee given that they ordered a cake?

• 0.50

• 0.40

• 0.10

• 0.25

In a city, 40% of the population owns a car, and 10% of car owners also own a motorcycle. What is the probability that a randomly selected person owns a motorcycle given that they own a car?

• 10%

• 20%

• 5%

• 15%

A survey shows that 50% of teenagers use social media, and 20% of those who use social media also play video games. What is the probability that a teenager plays video games given that they use social media?

• 0.20

• 0.50

• 0.30

• 0.10

In a bag of marbles, 30% are red and 10% of the red marbles are large. What is the probability that a marble is large given that it is red?

• 0.1

• 0.2

• 0.5

• 0.3

A local gym has 150 members, 90 of whom attend yoga classes and 60 attend weight training. If a member is chosen at random, what is the probability that they attend weight training given that they attend yoga classes?

• 0

• 0.25

• 1

• 0.5

In a survey, 75% of adults own a smartphone, and 50% of smartphone owners use it for online shopping. What is the probability that an adult uses their smartphone for online shopping given that they own a smartphone?

• 0.25

• 0.75

• 1.0

• 0.5