Question

If S is the sample space and P(A) = $\frac{1}{3}$ P(B) and S = A ∪ B, where A and B are two mutually exclusive events, then P (A) =
(a) 1/4
(b) 1/2
(c) 3/4
(d) 3/8

Answer 1

Let S be he sample space such that S = A∪B P(S) = 1 where A and B are mutually exclusive
$$\begin{gathered} \mathrm{Also}\mathrm{given}P\left(A\right)=\frac{1}{3}P\left(B\right) \\ \mathrm{i}.\mathrm{e}P\left(B\right)=3P\left(A\right) \end{gathered}$$
Since P(A∪B) = P(A) + P(B) (∵ A and B are mutually exclusive)
i.e. P(S) = P(A) + 3P(A)
i.e.1 = 4 P(A)
i.e. P(A) = $\frac{1}{4}$
Hence, the correct answer is option A.