Question

In a standard deck of 52 cards。

(a) What are the total number of five card hands?
(b) What is the probability of having exactly two Aces?
(c) What is the probability of getting a hand containing five Two’s?
(d) What is the probability of a Three given that the first four cards are not a Three?

Answer 1

a)

total number of five card hands = 52C5 = 2598960

b)

So we have 5 cards,out of which 2 has to be aces

So favourable ways = selecting 2 aces from 4 + selecting 3 cards from rest 48 cards

                              = 4C2 + 48C3

                              =17302

So Probability = 17302/2598960

                              =0.006657

c)

Since in a deck,we have only four 2's,so probability of getting a hand containing five two's is 0

d)

favourable ways = selecting 4 cards from 52 cards + selecting a three from 4 cards of three

                              = 52C4 + 4C1

                              =270729

So probability =270729/2598960

                              =0.104168