Question

Let A and B be two independent events such that $P\left(A\right)=\frac{1}{3}$ and $P\left(B\right)=\frac{1}{4}$
$\begin{array}{cccc}& ListI& & ListII\\ P.& P(A\cup B)isequalto& 1.& \frac{1}{2}\\ Q.& P\left(\frac{A}{A\cup B}\right)isequalto& 2.& \frac{2}{3}\\ R.& P\left(\frac{B}{A^{\prime }\cap B^{\prime }}\right)isequalto& 2.& \frac{1}{3}\\ S.& P\left(\frac{A}{B}\right)isequalto& 4.& 0\end{array}$

• A. P-1; Q-3; R-2; S-4
• B. P-2; Q-1; R-4; S-3
• C. P-1; Q-2; R-4; S-3
• D. P-2; Q-3; R-1; S-4

Answer 1

The correct option is C P-1; Q-2; R-4; S-3

$P\left(A\right)=\frac{1}{3},P\left(B\right)=\frac{1}{4}$
(P) $P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$
$=\frac{1}{3}+\frac{1}{4}-\frac{1}{12}=\frac{1}{2}$
(Q) $P\left(\frac{A}{A\cup B}\right)=\frac{P\left(A\right)}{P(A\cup B)}=\frac{2}{3}$
(R) $P\left(\frac{B}{A^{\prime }\cap B^{\prime }}\right)=\left(\frac{P\left(\varphi \right)}{P(A^{\prime }\cap B^{\prime })}\right)=0$
(S) $P\left(\frac{A}{B}\right)=P\left(A\right)=\frac{1}{3}$