Five cards are drawn from an ordinary 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 required probability is 0.00144 or 0.144%.

Step-by-step explanation:

Consider the provided information.

Five cards are drawn from an ordinary deck of 52 playing cards.

A full house is a hand that consists of two of one kind and three of another kind.

The total number of ways to draw 5 cards are:

Now we want two of one kind and three of another.

Let the hand has the pattern AAABB, where A and B are from distinct kinds. The number of such hands are:

Thus, the required probability is:

Hence, the required probability is 0.00144 or 0.144%.