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) $P(A^{\prime }\cap B^{\prime })$
(ii) $P(A\cap B’)$

	(i)	(ii)
(a)	0.12	0.19
(b)	0.19	0.12
(c)	0.13	0.20
(d)	0.19	0.18

• A. a
• B. b
• C. c
• D. d

Answer 1

Answer: (A)

Here, $P\left(A\right)=0.54$,
$P\left(B\right)=0.69$ and
$P\left(A\cap B\right)=0.35$
$\left(i\right)P\left(A^{\prime }\cap B^{\prime }\right)=P\left(\overline{A\cup B}\right)=1-P\left(A\cup B\right)$
$=1-\left[P\left(A\right)+P\left(B\right)-P\left(A\cap B\right)\right]$
$=1-\left[0.54+0.69-0.35\right]$
$=1-0.88$
$=0.12$
$\left(ii\right)P\left(A\cap B^{\prime }\right)=P\left(A\right)-P\left(A\cap B\right)$
$=0.54-0.35$
$=0.19$