Mathematics

Problem

In a school, let •

A

= “a student studies Mathematics” with

P(A)=0.30

, •

B

= “the same student plays football” with

P(B)=0.25

. The events

A

and

B

are independent. Find: (i)

P(B \mid A)

(ii)

P(A \cap B)

Intuitive explanation

When two events are independent, knowing that one happened tells you nothing about the probability of the other—the conditional probability equals the unconditional one. This independence also gives you a direct formula for their intersection: just multiply the individual probabilities. These two results are the foundation of working with independent events.

Intuitive explanation

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