Problem 10.Wayne is interested in two games, Keno and Bolita. To play Bolita, he buys a ticket for $1 marked with a number 1 .. 100, and one ball is drawn randomly from a collection marked with the numbers 1, ..., 100. If his ticket number matches the number on the drawn ball, he wins $75; otherwise he gets nothing. To play Keno, he buys a ticketfor $1marked with the numbers 1 .. 4 and there are only 4 balls, marked 1, ..., 4; if he wins he gets $3; otherwise he gets nothing.

(a) What is the expected payout (expected value of net profit after buying ticket and possibly winning something) for each of these games?

(b) What is the variance and standard deviation for each of these games?

(c) If Wayne has forgotten everything he ever learned about probability theory and he decides to play one (and only one) of these games for a very long time, which one should he choose? Or does it not matter?

(d) If Wayne has probability amnesia only for a short time, and he decides to try one of these games a couple of times, just for fun, which one should he choose?