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## Statistics and probability

### Course: Statistics and probability>Unit 7

Lesson 9: Conditional probability and independence

# Dependent and independent events

You might need: Calculator

## Problem

There are 150 students in an eleventh grade high school class. There are 45 students in the soccer team and 35 students in the basketball team. Out of these students, there are 20 who play on both teams.
Let A be the event that a randomly selected student in the class plays soccer and B be the event that the student plays basketball. Based on this information, answer the following questions.
What is P, left parenthesis, A, right parenthesis, the probability that the student plays soccer?
What is P, left parenthesis, B, right parenthesis, the probability that the student plays basketball?
What is P, left parenthesis, A, start text, space, a, n, d, space, end text, B, right parenthesis, the probability that the student plays soccer and basketball?
What is P, left parenthesis, A, start text, space, vertical bar, space, end text, B, right parenthesis, the conditional probability that the student plays soccer given that he or she plays basketball?
Is P, left parenthesis, A, start text, space, vertical bar, space, end text, B, right parenthesis, equals, P, left parenthesis, A, right parenthesis? Are the events A and B independent?