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) $P(A \cap B’)$

	(i)$ \qquad$	(ii) $ \qquad$
(a) $ \quad$	0.12$ \quad$	0.19$ \quad$
(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'\cap B'\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'\right)=P\left(A\right)-P\left(A\cap B\right)$
$=0.54-0.35 $
$=0.19$