Question

If A and B are two events such that $P(A\cup B)+P(A\cap B)=\frac{7}{8}$ and P(A) = 2 P(B), then P(A)______________.

Answer 1

For two events A and B,
given, P(A⋃B) + P(A⋂B) = $\frac{7}{8}$
P(A) = 2 P(B)
then using,
P(A⋃B) = P(A) + P(B) – P(A⋂B)
i.e P(A⋃B) + P(A⋂B) = $\frac{1}{2}$P(A) + P(A)
$$\begin{gathered} \mathrm{i}.\mathrm{e}\frac{7}{8}=\frac{3}{2}P\left(A\right) \\ \mathrm{i}.\mathrm{e}P\left(A\right)=\frac{7}{12} \end{gathered}$$