[Helpplease7890]

Any help would be greatly appreciated. The problem is: Rock-paper-scissors is a hand game that is played by two people. The players count to three in
unison and simultaneously \throw" one of three hand signals that correspond to rock, paper or
scissors. The winner is determined by the rules: rock smashes scissors, scissors cuts paper, and
paper covers rock. Because a tie happens around 1/3 of the time, several variants of
Rock-Paper-Scissors exist that include more choices to make ties more unlikely.

Rock=A
Scissors=B
Lizard=C
Paper=D
Spock=E

Rock-paper-scissors-lizard-Spock (RPSLS) is a variant of rock-paper-scissors that allows vs choices.
Each choice wins against two other choices, loses against two other choices, and ties against itself.
In the above gure as you progress clockwise, each object wins against the next two objects. Rock
smashes scissors and crushes lizard, scissors decapitates lizard and cuts paper, lizard eats paper
and poisons Spock, paper disproves Spock and covers Rock, and nally Spock vaporizes rock and
smashes scissors.
1. Two roommates, roommate 1 and roommate 2, are arguing over who should clean the dishes
and they decide to play a game of RPSLS to settle the dispute. Let fA1;B1;C1;D1;E1g
represent roommate 1's choices and fA2;B2;C2;D2;E2g represent roommate 2's choices based
on the notation in the gure.
(a) List the possible outcomes using the above notation... for instance (A1;A2) is when both
roommates throw rock and tie, and (A1;B2) is when roommate 1 throws rock and room-
mate two throws scissors 􀀀! Roommate 1 wins.
(b) List the outcomes where roommate 1 wins.
(c) List the outcomes where the game ends in a tie.
2. Assume both roommates' choices of rock, paper, scisors, lizard, or Spock are random, inde-
pendent, and equally likely.
(a) What is the probability roommate 1 wins?
(b) What is the probability of a tie?
3. Assume roommate 1's choices of rock, paper, scisors, lizard, or Spock are random, independent,
and equally likely. However, lets assume that roommate 2 is a huge Star Trek fan and will
throw Spock 40% of the time with the remaining four choices remaining equally likely.
(a) Under these conditions, what is the probability roommate 1 wins?
(b) Under these conditions, what is the probability of a tie?