# While shuffling a pack of 52 playing cards,

Question:

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

A. $\frac{29}{52}$

B. $\frac{1}{2}$

C. $\frac{26}{51}$

D. $\frac{27}{51}$

Solution:

C. 26/51

Explanation:

We know that, in a pack of 52 cards 26 are of red colour and 26 are of black colour.

It is given that 2 cards are accidentally dropped

So,

Probability of dropping a red card first $=\frac{26}{52}$

Probability of dropping a red card second $=\frac{26}{51}$

Similarly,

Probability of dropping a black card first $=\frac{26}{52}$

Probability of dropping a black card second $=\frac{26}{51}$

$\therefore P$ (both cards of different colour) $=\frac{26}{-2} \times \frac{26}{-1}+\frac{26}{-2} \times \frac{26}{-1}$

$=2 \times \frac{26}{52} \times \frac{26}{51}$

$=\frac{26}{51}$

Hence, the correct option is (C).

$\therefore P$ (both cards of different colour) $=\frac{26}{52} \times \frac{26}{51}+\frac{26}{52} \times \frac{26}{51}$

$=2 \times \frac{26}{52} \times \frac{26}{51}$

$=\frac{26}{51}$

Hence, the correct option is (C).