Two cards are drawn without replacement from a standard deck

Two cards are drawn without replacement from a standard deck of 52 playing cards. What is the probability of choosing a red card for the second card drawn, if the first card, drawn without replacement, was a heart? Express your answer as a fraction or a decimal number rounded to four decimal places.

Solution

Total cards = 52

Number of red cards = 26

Number of hearts = 13

P(second card is red | first card was a heart) = P(first card is heart and second card is red) / P(first card is heart)

                                                                        = (13/52 * 25/51) / (13/52)

                                                                       = 25/51 (ans)