Question

In a card game, suppose a player needs to draw two cards without replacement of the same suit in order to win. Of the 52 cards, there are 13 cards in each suit. Suppose first the player draws a heart. Find the probability that the second card is not a heart.

Answer 1

Solution :

Number of hearts in a deck of 52 cards = 13

Total number of cards = 52

Since, two cards are to be drawn without replacement and one heart is already drawn, therefore now we are left with total 51 cards in which there are 12 cards of heart.

Hence, the probability that second drawn card is a heart = 12/51

Hence, the probability that second drawn card is not a heart = 1 - (12/51)

= (51 - 12)/51

= 39/51

= 13/17

= 0.7647

The probability that the second card is not a heart is 0.7647.