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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 $P\left(A\right)$, the probability that the student plays soccer?
What is $P\left(B\right)$, the probability that the student plays basketball?
What is , the probability that the student plays soccer and basketball?
What is , the conditional probability that the student plays soccer given that he or she plays basketball?
Is ? Are the events $A$ and $B$ independent?