A pack of cards contains 4 aces, 4 kings, 4 queens and 4 jacks. Two cards are drawn at random. proba

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14.Probability

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A pack of cards contains $4$ aces, $4$ kings, $4$ queens and $4$ jacks. Two cards are drawn at random. The probability that at least one of these is an ace, is

A

$\frac{9}{{20}}$

B

$\frac{3}{{16}}$

C

$\frac{1}{6}$

D

$\frac{1}{9}$

Solution

(a) Required probability is $1 – P$ (No Ace)

$ = 1 – \frac{{{}^{12}{C_2}}}{{{}^{16}{C_2}}} = 1 – \frac{{12\,\,.\,\,11}}{{16\,\,.\,\,15}} = \frac{9}{{20}}.$

Standard 11

Mathematics

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