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14.Probability
easy
‘$A$’ draws two cards with replacement from a pack of $52$ cards and ‘$B$' throws a pair of dice what is the chance that ‘$A$’ gets both cards of same suit and ‘$B$’ gets total of $6$
A
$\frac{1}{{144}}$
B
$\frac{1}{4}$
C
$\frac{5}{{144}}$
D
$\frac{7}{{144}}$
Solution
(c) The probaility of drawing two cards of same suit
$ = \frac{{13}}{{52}} \times \frac{{13}}{{52}}$ and it can be of any suit out of $4$.
So $P(A) = \frac{{4 \times 13 \times 13}}{{52 \times 52}} = \frac{1}{4}$ and
$P(B) = \frac{5}{{36}}$
Thus $P(A \cap B) = P(A)\,.\,P(B) = \frac{1}{4} \times \frac{5}{{36}} = \frac{5}{{144}}.$
Standard 11
Mathematics
