Two cards are drawn at random and one-by-one without replacement from a well-shuffled pack of 52 playing cards. Find the probability that one card is red and the other is black.

We know that 52 cards are in the one pack.

We also know that there are 26 number of red cards and 26 numbers of black cards.

Now, the required probability is

The probability of one card is red and the other is black

= The probability of first card is red and second is black + The probability of first card is black and second is red
$\begin{array}{l}=\frac{26}{52}\times \frac{26}{51}+\frac{26}{52}\times \frac{26}{51}\\ =\frac{13}{51}+\frac{13}{51}=\frac{26}{51}\end{array}$
Therefore, the probability of one card is red and the other is black is $\frac{26}{51}.$