Question

In a certain card? game, players begin each round with 3 cards in? hand, and then draw 7 more over the course of the round. If a player starts a round with 2? hearts, what is the probability that the player will have 7 or more hearts by the end of the? round?

Answer 1

Assuming the card game used a standard deck of 52 cards which has 13 heart cards.

After beginning the game with 3 cards in hand, 49 cards are left out of which 7 cards are drawn.

Now, if there are 2 heart cards at the start of round there will be 11 heart cards and 38 non heart cards left

Thus to have 7 or more cards by the end of the round, player should have drawn 5 or more heart cards out of the 7 cards drawn.

Thus, required probability = P(5 heart cards) + P(6 heart cards) + P(7 heart cards)

= (11C5 × 38C2 + 11C6 × 38C1 + 11C7)/49C7

= 0.003989