Please show all work Suppose that you select 2 cards without

Please show all work.

Suppose that you select 2 cards without replacement from a standard deck of 52 playing cards.

a) If the first card that you select is not a seven, what is the probability that the second card that you select is a seven?

b) If the first card that you select is a heart, what is the probability that the second card that you select is a nine?

Solution

a)

First card not a seven. Therefore, remaining no of cards are 51 and there are 4 Sevens in the deck

Therefore, required probablity = 4/51

b)

First card selected is a heart. In this case, we shall divide the problem in two parts. The first part is when the card is the nine of hearts and the second is when it is not.

Part 1:

51 cards remaining, 3 of them Nines. Therefore, required probability = 3/ 51

Part 2:

51 cards remaining, 4 of them Nines. Therefore, required probability = 4/51

Therefore, probability = (0.5*3+0.5*4)/51 = 3.5/51 = 7/102