Let $A$ and $B$ be events such that $P(A)=\frac12$, $P(B)=\frac34$ and \(P(A\cup B)=\frac78\

Question

Let $A$ and $B$ be events such that $P(A)=\frac12$, $P(B)=\frac34$ and $P(A\cup B)=\frac78$. Calculate $P(A ∩ B)$. Calculate $P(A|B)$. Are the events A and B independent? Give a reason for your answer.

Accepted Answer

$P(A\mid B)=\frac{3/8}{3/4}=\frac12$. Since $P(A)P(B)=\frac38=P(A\cap B)$, the events are independent.

Calculate intersection and conditional probability and test independence.

Calculate intersection and conditional probability and test independence.

Solution:

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