Probability 3 Question 30
30. Let $A$ and $B$ be two events such that $P(A)=0.3$ and $P(A \cup B)=0.8$. If $A$ and $B$ are independent events, then $P(B)=\ldots$.
(1990, 2M)
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Solution:
- $P(A \cup B)=P(A)+P(B)-P(A) P(B)$, as $A$ and $B$ are independent events.
$$ \begin{array}{ll} \Rightarrow & 0.8=(0.3)+P(B)-(0.3) P(B) \\ \Rightarrow & 0.5=(0.7) P(B) \Rightarrow P(B)=\frac{5}{7} \end{array} $$
