# Probability of independent events?

Suppose that A and B are independent events such that P(Ā) = 0.1 and P(B) = 0.4

Find P(A ∩ B) and P(A U B)

Thank you!

Relevance

Since P(Ā) = 0.1, P(A) = 0.9.

P(A ∩ B) = P(A) * P(B). That is the definition of independent events. So just multiply the two probabilities together.

P(A U B) is a little more complicated. It is equal to P(A) + P(B) for mutually exclusive events that can't both occur, but for independent events, they can both occur (with a probability calculated above).

The general expression is:

P(A U B) = P(A) + P(B) - P(A ∩ B)

so just use the value of P(A ∩ B) you calculated above.

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• P(A n B)=P(A) x P(B) = 0.1 x 0.4 = 0.04

P(A U B)= P(A) + P(B) = 0.1+0.4=0.5

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