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If $A$ and $B$ are two independent events such that $P(A)=0.3,
P(B)=x$ and $P(A \cup B)=0.44$, then $x=$
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P(B)=x$ and $P(A \cup B)=0.44$, then $x=$
Solution:
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Verified Answer
The correct answer is:
$0.2$
$P(A \cup B)=P(A)+P(B)-P(A \cap B)$
$\Rightarrow \quad 0.44=0.3+x-P(A \cap B)$
$\Rightarrow \quad 0.44-0.30=x-(P(A) \cdot P(B))$
$\begin{aligned} \Rightarrow \quad 0.14= & x-(0.3 x) \\ & {[\because A \text { and } B \text { are independent events and }}\end{aligned}$
$\therefore P(A) \cdot P(B)=P(A \cap B)]$
$\begin{aligned} \Rightarrow \quad & =0.7 x=0.14 \\ x & =\frac{0.14}{0.7}=0.2\end{aligned}$
$\Rightarrow \quad 0.44=0.3+x-P(A \cap B)$
$\Rightarrow \quad 0.44-0.30=x-(P(A) \cdot P(B))$
$\begin{aligned} \Rightarrow \quad 0.14= & x-(0.3 x) \\ & {[\because A \text { and } B \text { are independent events and }}\end{aligned}$
$\therefore P(A) \cdot P(B)=P(A \cap B)]$
$\begin{aligned} \Rightarrow \quad & =0.7 x=0.14 \\ x & =\frac{0.14}{0.7}=0.2\end{aligned}$
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