Two cards are drawn without replacement from a standard deck

Two cards are drawn, without replacement, from a standard deck of fifty-two cards. Find the probability of these events.

a. Getting a king on the first card and a king on the second card..

b. Getting a diamond on the first card and a diamond on the second card.

c. Getting a 10 on the first card and a 6 on the second card.

d. Getting a club on the first card and a spade on the second card.

Solution

a)

4C2 / 52C2 = 0.0045

b)

16C2 / 52C2 = 0.0905

c)

2C1 * 2C1 / 52C2   = 0.0030

d)

11C1 / 52C1    +   11C1 / 51C1 = 0.4272