Problem 147SE

Refer to Exercise 2.146. A gambler has been dealt five cards: two aces, one king, one five, and one 9. He discards the 5 and the 9 and is dealt two more cards. What is the probability that he ends up with a full house?

Reference

Five cards are drawn from a standard 52-card playing deck. What is the probability that all 5 cards will be of the same suit?

Solution :

Step 1 of 1:

Given a gambler has been dealt 5 cards.

Our goal is:

We need to find the probability that he ends up with a full house.

We know that a gambler has been dealt 5 cards.

If he is dealt two kings or an ace and a king.

There are 47 cards remaining in the deck, two of which are aces and three are kings

Then the probabilities of these events areand respectively.

Now we have to find the probability that he ends up with a full house.

So, the probability of full house is given by

+

The formula of the combinations is

Then,

3

Hence, 3.

1081

Hence =1081.

Similarly we get =3, =2.

Now we substitute all the values.

+

+

= 0.000832

Therefore, the probability that he ends up with a full house 0.000832.