Question

A bridge hand is found by takinf 13 cards at random and without replacement from a deck of 52 playing cards. Find the probability of drawing each of the following hands.

(a) One in which there are 5 spades, 4 hearts, 3 diamonds and 1club.

(b) One in which there are 5 spades, 4 hearts, 2 diamonds and 1 club.

(c) One in which there are 5 spades, 4 hearts, 2 diamond, and 3 clubs.

(d) Suppose you are dealt 5 cards of one suit, 4 cards of another. Would the probability of having the other suits split 3 and 1 be greater than the probability of having them split 2 and 2?

Answer 1

a) There are 13 spades out of which 5 are dealt, this implies that number of ways to do this =

There are 13 hearts out of which 4 are dealt, this implies that number of ways to do this =

There are 13 diamond out of which 3 are dealt, this implies that number of ways to do this =

There are 13 club out of which 1 are dealt, this implies that number of ways to do this =

Total number of ways =

Probability = = 0.005

Similarly

b)

There are 13 spades out of which 5 are dealt, this implies that number of ways to do this =

There are 13 hearts out of which 4 are dealt, this implies that number of ways to do this =

There are 13 diamond out of which 2 are dealt, this implies that number of ways to do this =

There are 13 club out of which 1 are dealt, this implies that number of ways to do this =

Total number of ways =

Probability = = 0.0045

c)

There are 13 spades out of which 5 are dealt, this implies that number of ways to do this =

There are 13 hearts out of which 4 are dealt, this implies that number of ways to do this =

There are 13 diamond out of which 2 are dealt, this implies that number of ways to do this =

There are 13 club out of which 3 are dealt, this implies that number of ways to do this =

Total number of ways =

Probability = = 0.0116