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

Options

•  1/5

•  3/16

•  9/20

• 1/9

   

Answer 1

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