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.

Accepted Solution

Answer:Sammy is expected to lose $1.39 on average per rollStep-by-step explanation:Since Sammy is rolling two six-sided cubes, the number of possible outcomes is given by:6 x 6 =36Out 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.