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 expected value of the game without considering cost

The wheel is divided into two equal - parts. The probability of landing on each part \(P=\frac{1}{2}\).
The formula for the expected value \(E(X)=\sum_{i = 1}^{n}x_{i}P(x_{i})\). Here, \(x_1 = 5\) and \(x_2=9\).

$$
LATEXBLOCK0
$$

Step2: Calculate the expectation considering the cost

The cost to play the game is \(C = 3\). The expectation \(E\) of a person who plays the game is \(E=E(X)-C\).
Substitute \(E(X) = 7\) and \(C = 3\) into the formula: \(E=7 - 3\)

Answer:

\(4\)