Question

A standard deck of cards is dealt to four players, each receiving thirteen cards. If the first player gets exactly five hearts, what is the chance the second player gets exactly four hearts?

Answer 1

0.000024

Explanation:

If the first player gets exactly five hearts, there are 39 cards left, 8 of which are hearts.

So, the probability of getting one heart is 8/39, for the second heart the probability is 7/38 and 6/37 and 5/36 for the 3rd and 4th hearts.

There are still 4 hearts in the deck, and the probability of getting a non heart is (35-4)/35=31/35, (34-4)/34=30/34,..., (27-4)/27=23/27 for the next 9 cards.

As the event of taking a card is independent of the previous result, the probability the second player gets exactly 4 hearts is

(8/39)*(7/38)*(6/37)*(5/36)*(31/35)*(30/34)***(23/27)

= 0.000024