Question

While shuffling a pack of $52$ playing cards, $2$ are accidentally dropped. The probability that the missing cards to be of different colours is

• A. $\frac{29}{52}$
• B. $\frac{1}{2}$
• C. $\frac{26}{51}$
• D. $\frac{27}{51}$

Answer 1

The correct option is C $\frac{26}{51}$

There are $26$ red cards and $26$ black cards
i.e., total number of cards $=52$
$P$ (both cards of different colours) is
$P\left(B\right)P\left(R\right)+P\left(R\right)P\left(B\right)$
$=\frac{26}{52}\times \frac{26}{51}+\frac{26}{52}\times \frac{26}{51}=2(\frac{26}{52}\times \frac{26}{51})=\frac{26}{51}$.

Hence, option C is correct.