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

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