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
$=\frac{{}^4{C}_1{\times }^{12}{C}_1}{{}^{16}{C}_2}+\frac{{}^4{C}_2}{{}^{16}{C}_2}$
$=\frac{4\times 12\times 2}{16\times 15}+\frac{4\times 3}{16\times 15}$
$=\frac{96+12}{16\times 15}=\frac{108}{240}$
$=\frac{9}{20}$