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$A$ and $B$ are two independent events such that $P(A \cup B)=0.8$ and $P(A)=0.3$. The $P(B)$ is
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Verified Answer
The correct answer is:
$\frac{2}{7}$
Hints : Let $\mathrm{P}(\mathrm{B})=x$
$$
\mathrm{P}(\mathrm{A} \cup \mathrm{B})=\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})-\mathrm{P}(\mathrm{A} \cap \mathrm{B})=0.3+(1-x)-0.3(1-x)
$$
or $\quad 0.8=1-x+0.3 x$
or $\quad 1-0.7 x=0.8$
or $\quad 0.7 x=0.2$
or $\quad x=\frac{2}{7}$
$$
\mathrm{P}(\mathrm{A} \cup \mathrm{B})=\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})-\mathrm{P}(\mathrm{A} \cap \mathrm{B})=0.3+(1-x)-0.3(1-x)
$$
or $\quad 0.8=1-x+0.3 x$
or $\quad 1-0.7 x=0.8$
or $\quad 0.7 x=0.2$
or $\quad x=\frac{2}{7}$
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