Question

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

Answer 1

(c) $\frac{9}{20}$

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) = $\frac{1}{20}+\frac{2}{5}=\frac{9}{20}$