Question

Out of a pack of 52 cards one is lost, from the remainder of the pack , two cards are drawn and are found to be spades .Find the chance that the missing card is a spade ?

• A. $\frac{11}{50}$
• B. $\frac{11}{49}$
• C. $\frac{10}{49}$
• D. $\frac{10}{50}$

Answer 1

The correct option is A

$\frac{11}{50}$

(probability of 2 drawn cards being spade when missing card is spade)/(probability of 2 drawn cards being spade when missing card is spade + probability of 2 drawn cards being spade when missing card is not spade)

= $\frac{(\frac{1}{4}\times \frac{{}^{12}{c}_2}{{}^{51}{c}_2})}{(\frac{1}{4}\times \frac{{}^{12}{c}_2}{{}^{51}{c}_2}+\frac{3}{4}\times \frac{{}^{13}{c}_2}{{}^{51}{c}_2)}}$
= $\frac{(12\times 11)}{(12\times 11+3\times 13\times 12)}=\frac{11}{50}$