Sammy is playing a board game. He rolls two number cubes, each numbered 1-6. If he rolls a sum of 3 he wins S60 dollars, otherwise he loses

$5 dollars. How much does Sammy expect to win or lose on average per roll.

Out of those 36 outcomes, only two would result in a sum of 3, rolling a 1 and 2 or a 2 and a 1. Therefore, the probability of winning (P(W)) and the probability of losing (P(L)) are:

[tex]P(W) = \frac{2}{36}= \frac{1}{18}\\P(L) = 1- \frac{1}{18}= \frac{17}{18}[/tex]

The expected value is defined as the sum of the product of the likelihood of each event by its payout:

[tex]EV = P(W)*\$ W + P(L)*\$ L\\EV = \frac{1}{18}*60 - \frac{17}{18}*5\\EV =- \$1.39[/tex]

Sammy is expected to lose $1.39 on average per roll.

Sammy is playing a board game. He rolls two number cubes, each numbered 1-6. If he rolls a sum of 3 he wins S60 dollars, otherwise he loses $5 dollars. How much does Sammy expect to win or lose on average per roll.

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Sammy is playing a board game. He rolls two number cubes, each numbered 1-6. If he rolls a sum of 3 he wins S60 dollars, otherwise he loses

$5 dollars. How much does Sammy expect to win or lose on average per roll.