Question

If $2$ cards are drawn from a well shuffled pack of $52$ cards, the probability that they are of the same colours without replacement is:

• A. $\frac{1}{2}$
• B. $\frac{26}{51}$
• C. $\frac{25}{51}$
• D. $\frac{25}{102}$

Answer 1

The correct option is C $\frac{25}{51}$

The probability that both are red will be
$=\frac{26}{52}\times \frac{25}{51}$
$=\frac{25}{102}$
Similarly The probability that both are black will be
$=\frac{26}{52}\times \frac{25}{51}$
$=\frac{25}{102}$
Hence both the cards can be either red or black. Therefore the required probability is
$P\left(B\right)+P\left(R\right)$
$=\frac{25}{102}+\frac{25}{102}$
$=\frac{25}{51}$.