Management Aptitude Test 2015 Paper

(c) In a pack of 52 cards, there are 13 diamonds.
Probability of getting diamonds = $\frac{13}{52}=\frac{1}{4}$
But one card is lost.
Probability (getting two diamonds) = $\frac{{}_{}^{13}{\mathit{C}}_2^{}}{{}_{}^{51}{\mathit{C}}_2^{}}$
= $\frac{13\times 12}{51\times 50}=\frac{26}{425}$
Which is the probability of getting two diamonds when card lost is not diamond.
Probability of that card is diamond
= 1 - $\frac{26}{425}=\frac{399}{425}=\frac{23}{25}$