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Suppose you roll two fair dices. If the two dices give the same number of dots...

Suppose you roll two fair dices. If the two dices give the same number of dots facing up (a pair of one, two, three, four, five, but not six), you win $20; if the two dices give a pair of six, you win an amazing $100; otherwise you lose $7. In terms of profits and statistics, should you play the game? Why or why not?

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Answer #1

Probability distribution for the question is given as

X P(X) Outcome
$20 5/36 (1,1),(2,2),(3,3),(4,4),(5,5)
$100 1/36 (6,6)
-$7 30/36 36-(1+5) = 30

Expected value =

= $20*(5/36)+$100*(1/36)-$7*(30/36)

= $2.78 + $2.78 - $5.83

= -$0.28 (rounded to 2 decimals)

Expected value is negative, so I will not play this game.

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