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 - sized sections. So the probability of landing on $\$6$ is $P(6)=\frac{1}{2}$, and the probability of landing on $\$12$ is $P(12)=\frac{1}{2}$.

Step2: Calculate the expected value of the game without considering the cost

The formula for the expected value $E(X)=\sum_{i}x_{i}P(x_{i})$. Here, $x_1 = 6$ and $x_2=12$.

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Step3: Calculate the expected value of the game considering the cost

The cost to play the game is $C = 3$. The expected value of the game for the player is $E=E(X)-C$.

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Answer:

$6.00$