‘ A ’ draws two cards with replacement from a pack of 52 cards and ‘ B ' throw

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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

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(IIT-1998)