Question

If \(P(X)=0.33, P(Y)=0.75\), and \(P(X \cap Y)=0.30\), are \(X\) and \(Y\) independent?

Answer 1

Events \(X\) and \(Y\) are not independent.

 

Explanation:

If \(X\) and \(Y\) are independent event then:

\(P(X) \cdot P(Y) = P(X\cap Y)\)

Given that \(P(X)=0.33, P(Y)=0.75\), and \(P(X \cap Y)=0.30\), then:

\(P(X) \cdot P(Y) =0.33\cdot 0.75 = 0.2475\), but  \(P(X \cap Y)=0.30\)

\(\therefore P(X) \cdot P(Y) \neq P(X\cap Y)\)

hence events \(X\) and \(Y\) are not independent.