Question 1:

A typical deck of cards has 4 suits (,,, - and the following 13 denominations: Ace, 2 thru 10, Jack, Queen, and king). A single card has two characteristics suit and denomination, for example [King of ] or [4 of ] etc. ["2 thru 10" is taken to mean a 2, 3, 4, 5, 6, 7, 8, 9 or, 10 and "face-card" is taken to mean a Jack, Queen or King]

a. Say 8 cards are randomly selected without replacement from your deck of 52-card deck. Let X be the number of 's drawn. What is the Standard Deviation of X.

b. If 30 cards are selected with replacement find the probability that the number of 's drawn is at most 8 but at least 5.

c. If cards are selected with replacement what is the probability of needing to draw a total of 17 times in order to see any "face card," exactly seven times?

d. If cards are selected with replacement how many times do you expect you will need to draw until seeing the first "2 thru 10"card?