In a casino game, a die is rolled until two sixes have shown. (a) One bet you ca
ID: 3217733 • Letter: I
Question
In a casino game, a die is rolled until two sixes have shown. (a) One bet you can make on this game costs $15, regardless of outcome, and has payout as follows. For each time the die is rolled during the game, you get $1. What are the expected winnings (losses count negative) for this bet? (b) A different bet that the casino offers costs $5, and has payout as follows. If the total number of die rolls in the game is odd, then you get $10, and otherwise you get nothing. (Or you can think of wagering $5, and on the event of an odd number of rolls you get your wager back and an additional $5, and on the event of an even number of rolls you lose your $5 wager.) What are the expected winnings (losses count negative) for this bet?Explanation / Answer
A) Expected number of rolls till two sixes are shown = 2x6 = 12
Expected winnings = 12-15 = -$3
(a loss of $3)
B) P(odd number of rolls) = 0.5
P(even number of rolls) = 0.5
So, expected winnings = 0.5x10 - 5 = $0