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you are thinking of playing a game with a pair of dice. you will win if...

you are thinking of playing a game with a pair of dice. you will win if the sum of the top faces is either 7 or 8. the loser pays the winner $1 each game. should you play? set up a probability distribution table and use it to find your expected earnings. Then make your decisions.

Math   Statistics-And-Probability   
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Answer #1

Total number of cases possible = 6x6 = 36

Sum is 7 in the following cases: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1)

P(sum is 7) = 6/36 = 1/6

Sum is 8 in the following cases: (2,6), (3,5), (4,4), (5,3), (6,2)

P(sum is 8) = 5/36

P(Sum is 7 or 8 when rolling a dies) = P(sum is 7) + P(sum is 8)

= 6/36 + 5/36

= 11/36

P(losing the game) = 1 - 11/36 = 25/36

Winning($) 1 -1
P(winning) 11/36 25/36

Expected value of the game = 1x11/36 + -1x25/36

= $ -14/36

The expected value is negative. So, you should not play this game.

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