If $P ( A ) = .55 , P ( B \mid A ) = .4 , P ( A \cap B ) = .22$, and $A$ and $B$ are independent events, find $P ( B )$.
A) $.4$
B) $.55$
C) $.88$
D) $.22$

Name: If $P ( A ) = .55 , P ( B \mid A ) = .4 , P ( A \cap B ) = .22$, and $A$ and $B$ are independent events, find $P ( B )$. A) $.4$ B) $.55$ C) $.88$ D) $.22$
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Quizplus · Accepted Answer

For independent events $A$ and $B$, $P(A \cap B) = P(A) \times P(B)$. Given $P(A \cap B) = .22$ and $P(A) = .55$, we find $P(B) = \frac{P(A \cap B)}{P(A)} = \frac{.22}{.55} = .4$.

If P(A)=.55,P(B∣A)=.4,P(A∩B)=.22P ( A ) = .55 , P ( B \mid A ) = .4 , P ( A \cap B ) = .22P(A)=.55,P(B∣A)=.4,P(A∩B)=.22

If $P ( A ) = .55 , P ( B \mid A ) = .4 , P ( A \cap B ) = .22$