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Unit 01 /
Problem 3:


F computing probabilities with independent events
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Easy


Let $A$ and $B$ be two independent events with $P(A)=0.4$ and $P(A\cup B)=0.64$. What is $P(B)$?

Answer:

$0.4$

Solution:

From the addition rule, we get\[\begin{align}&P(A\cup B)=P(A)+P(B)-P(A\cap B)\\
\implies &P(A\cup B)=P(A)+P(B)-P(A)P(B),\text{ since independent}\\
\implies &P(A\cup B)=P(A)+[1-P(A)]P(B)\\
\implies &P(B)=\frac{P(A\cup B)-P(A)}{1-P(A)}\\
\implies &P(B)=\frac{0.64-0.4}{1-0.4}=\frac{0.24}{0.6}=0.4.\end{align}\]