In rolling a pair of dice, suppose you win $5 if the sum is 10 but lose $2 if the roll is "doubles." If the price to play is $1, would it be a fair game? Justify your answer.

Answer 1

The probability of throwing a "10" with a pair of dice is 3/36 = 1/12. The probability of throwing "doubles" is 6/36 = 1/6.

Probable gain for $1 bet =
(1/12)*5 - (1/6)*2 = $ 1/12

The game favors the bettor