You draw five cards at random from a standard deck of 52 playing cards. what is the probability that the hand drawn is a full house? (a full house is a hand that consists of two of one kind and three of another kind.)

The probability that the hand drawn is a full house is 0.00144.

Step-by-step explanation:

In a full house we have a hand that consists of two of one kind and three of another kind, i.e 5 cards are selected.

The number of ways of selecting 5 cards from 52 cards is:

In a deck of 52 cards there are 13 kind of cards, namely{K, Q, J, A, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

Two kinds can be selected in, ways

One of the two kinds can be selected for 3 cards combination in ways.

There are 4 cards of each kind.

So 3 cards combination can be selected from any of the two kinds in ways.

And 2 cards combination can be selected from any of the two kinds in ways.

Thus, total number of ways to select a full house is:

The probability that the hand drawn is a full house is:

Thus, the probability of playing a full house is 0.00144.