1. Determine whether each random variable described below satisfies the conditions for a binomial setting, a geometric setting, or neither. Justify your answer in each case. (a) Draw a card from a standard deck of 52 playing cards, observe the card, return the card to the deck, and shuffle. Count the number of times you draw a card in this manner until you observe a jack. (b) Joey buys the same type of Virginia lottery ticket every week. X is the number of times in a year that he wins a prize. 2. When a computer generates random digits, the probability that any particular digit in the set {0, 1, 2, ...,9} is generated on any individual trial is 1/10 = 0.1. Suppose that we are generating digits one at a time and are interested in tracking occurrences of the digit 0. (a) Determine the probability that the first 0 occurs on the fifth random digit generated. (b) How many random digits would you expect to have to generate in order to observe the first 0