Sam and Frodo are playing a game where Frodo has 2 rings. In one round, Frodo puts his hands under the table, then places one ring on a random finger of his left hand and one ring on a random finger of his right hand. Sam has to guess which finger of each hand has a ring in order to win a round. LetXbe the number of rounds that Sam wins in 10 rounds. (a) FindPr(X<3). (b) FindEx(X). (c) Now they decide to play until Sam wins, and letYbe the number of rounds that they play. What isEx(Y)? (d) Suppose Sam has lost the last three rounds. How many more rounds does he expect to play until he wins?
