Question

for the wheel pictured on the right, assume that a person spins the pointer and is awarded the amount indicated by the pointer. if it costs $3 to play the game, determine (a) the expectation of a person who plays the game and (b) the fair price to play the game.

a. what is the expectation? $
(round to the nearest cent as needed.)

Explanation:

Step1: Calculate the probability of each outcome

The wheel is divided into 2 equal - parts. So the probability of landing on $10$, \(P(10)=\frac{1}{2}\), and the probability of landing on $9$, \(P(9)=\frac{1}{2}\). The cost to play the game is $C = 3$.

Step2: Use the formula for expected value

The formula for expected value \(E\) of a game is \(E=\sum_{i}(x_{i}P(x_{i}))-C\), where \(x_{i}\) are the outcomes and \(P(x_{i})\) are their probabilities.
Substitute \(x_1 = 10\), \(P(x_1)=\frac{1}{2}\), \(x_2 = 9\), \(P(x_2)=\frac{1}{2}\) and \(C = 3\) into the formula:

$$
LATEXBLOCK0
$$

Answer:

\(6.50\)