Question

A and B are two events such that P(A) = 0.54, P(B) = 0.69 and P(A \cap B) = 0.35.
Find
(i) $P(A\cap B)$ (ii) P $(A^{\prime }\cap B^{\prime })$ (iii) P $(A\cap B^{\prime })$
(iv) P $(A\cap B^{\prime })$

Answer 1

Here P(A) = 0.54, P(B) = 0.69
and $P(A\cap B)=\mathrm{0.35.}$
(i) We know that
$P(A\cup B0=P(A)+P(B)-p(A\cap B)=0.54+0.69-0.35=1.23-0.35=0.88$
$\left(ii\right)P(A^{\prime }\cap B^{\prime })=P\overline{(A\cup B)}=1-P(A\cup B)=1-0.88=0.12\left(iii\right)P(A\cap B^{\prime })=P\left(A\right)-P(A\cap B)=0.54-0.35=0.19$
$\left(iv\right)P(B\cap A^{\prime })$ = P(B) - P(A \cap B) \\
= 0.69 - 0.35 = 0.34.\)