Question

A game is played with a single fair die. A player wins $20 if a 2 turns up, $40 if a 4 turns up, and loses $30 if a 6 turns up. If any other face turns up, there is no winning. Find the expected sum of money the player can win.A)$3B) $4C) $5D) $6.50

Answer 1

The dice has 6 faces numbered 1 to 6.

The probability of landing any number is 1/6.

The expected value is the sum of products of the probability and the winnings/losings.

So the expected value in this case is given by:

`\begin{gathered} E(X)=(1)/(6)*20+(1)/(6)*40+(1)/(6)*(-30)+(1)/(6)*0+(1)/(6)*0+(1)/(6)*0 \\ E(X)=(20+40-30)/(6) \\ E(X)=5 \end{gathered}`

So the player can expect to win $5 per game in the long run.

Option C is correct.