Question

A pack of cards contains 4 aces, 4 kings, 4 queens and 4 jacks. Two cards are drawn at random from this pack without replacement. The probability that atleast one of them will be an aces, is

• A. $ \frac{1}{5} $
• B. $ \frac{3}{16} $
• C. $ \frac{9}{20} $
• D. $ \frac{1}{9} $

Answer 1

Answer: (C)

Total cards in the pack =16 Number of ways of selecting two cards randomly $ {{=}^{16}}{{C}_{2}} $
$ \therefore $ Probability of getting atleast one ace
$ =\frac{^{4}{{C}_{1}}{{\times }^{12}}{{C}_{1}}}{^{16}{{C}_{2}}}+\frac{^{4}{{C}_{2}}}{^{16}{{C}_{2}}} $
$ =\frac{4\times 12\times 2}{16\times 15}+\frac{4\times 3}{16\times 15} $
$ =\frac{96+12}{16\times 15}=\frac{108}{240} $
$ =\frac{9}{20} $