Question

Two cards are drawn from a well shuffled pack of 52 cards, one after another without replacement. Find the probability that one of these is red card and the other a black card?

Answer 1

$$\begin{gathered} P\left(\text{one red and one black}\right)=P\left(\text{first red and second black}\right)+P\left(\text{first black and second red}\right) \\ =\frac{26}{52}\times \frac{26}{51}+\frac{26}{52}\times \frac{26}{51}\left[\text{Without replacement}\right] \\ =\frac{13}{51}+\frac{13}{51} \\ =\frac{26}{51} \end{gathered}$$