Question

A game consists of rolling two dice. The game costs $2 to play. You roll a two dice. If the outcome totals 9 you get $10. Otherwise, you lose your $2. Should you play the game? Explain using probability.

Answer 1

Total number of outcomes = 6x6 = 36

Number of outcomes that totals 9 = 4                {(3,6), (4,5), (5,4), (6,3)}

P(outcome total 9) = 4/36 = 1/9

P(winning) = 1/9

P(losing) = 1 - 1/9 = 8/9

Expected outcome = winning amount x P(winning) - losing amount x P(losing)

= (10-2) x 1/9 - 2 x 8/9

= -8/9

= $-0.89

The expected outcome of the game is negative, meaning that you are expected to lose money. So, you should not play the game.