Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# 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 them is an ace is (a) 1/5 (b) 3/16 (c) 9/20 (d) 1/9 - Mathematics

MCQ

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 them is an ace is

•  1/5

•  3/16

•  9/20

• 1/9

#### Solution

$\frac{9}{20}$ We have:
P(both are aces) = $\frac{{}^4 C_2}{{}^{16} C_2} =$

$\frac{4}{16} \times \frac{3}{15} = \frac{1}{20}$ P(one is ace) = $\frac{{}^4 C_1 \times^{12} C_1}{C {{}^{16}}_2} = \frac{2}{5}$

∴ P(at least one is ace) = $\frac{1}{20} + \frac{2}{5} = \frac{9}{20}$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 33 Probability
Q 15 | Page 72