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. 11/50
• B. 11/49
• C. 10/49
• D. 10/50

Answer 1

The correct option is A

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)

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