Two cards are drawn one by one without replacement from a well shuffled pack of 52 cards. What is the probability that one is a red card and the other is a black card?

Solution

P(red card is first draw and black card in second draw) = $26 over 52 cross times 26 over 51 space equals 13 over 51$
P(black card is first draw and red card in second draw) = $26 over 52 cross times 26 over 51 space equals 13 over 51$
$therefore$ required probability = $13 over 51 plus 13 over 51 space equals 26 over 51$