Question

One of a pack of $52$ cards has been 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.

Answer 1

Suppose lost card is spade:-
So $12$ cards remained out of $51$ cards
So probability of choosing out of $4$ suit$\Rightarrow \frac{1}{4}$
Probability of drawing two spade
$=\frac{12}{51}\times \frac{11}{50}$
Total no. of outcome$=\frac{13\times 12}{52\times 51}$
Required Probability$=\frac{\frac{12}{51}\times \frac{11}{50}\times \frac{1}{4}}{\frac{13}{52}\times \frac{12}{51}}$
$=\frac{11}{50}$