Question

A certain casino game has a wheel with 5 different animals on it. It costs $10 to bet on an animal, and

if the ticker stops on your animal, you win $20. Otherwise, you lose your $10. Find and interpret the
expected value of this game to you, the player.

Answer 1

Expected value = - $ 4

Explanation:

Number of animals on the wheel = 5

Number of animals the player can bet on = 1

The player will win if the ticker stops on the chosen animal. Since, only one animal can be chosen out of 5, the probability of winning will be =
`(1)/(5)`

If the ticker stops on any of the rest 4 animals, the player will lose. So the probability of losing will be =
`(4)/(5)`

If the ticker stops on chosen animal, the winning amount is $ 20, if the ticker lands on any of other animal, its a loss of $ 10.

We need to calculate the expected value of this game. Expected value is calculated by multiplying the probability of each outcome with the outcome and then adding these products.

So, for this case, the expected value will be:

(Probability of winning x Outcome on winning) + (Probability of losing x Outcome of losing)

Using the values, we get:

`E=(1)/(5)(20)+(4)/(5)(-10)=-4`

Minus sign has been used with 10, because the money is being lost.

Thus, the expected value of the game is - $ 4. This means, on average a player who will play the game is expected to lose about $ 4 per game