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.)
b. what is the fair price to play the game? $ (round to the nearest cent as needed.)

Explanation:

Step1: Calculate the probability of winning and losing

The probability of winning \( P(W)=\frac{40}{40 + 60}=\frac{40}{100} = 0.4\), and the probability of losing \( P(L)=\frac{60}{40+60}=\frac{60}{100}=0.6\).

Step2: Calculate the expectation

The formula for expectation \(E\) is \(E = x_1P(x_1)+x_2P(x_2)\), where \(x_1\) is the winning amount (\(x_1 = 10\)) and \(x_2\) is the losing amount (\(x_2=0\)).
\(E=(10\times0.4)+(0\times0.6)=4\)

Step3: Calculate the fair price

The fair price to play the game is equal to the expectation.

Answer:

a. The expectation is \(\$4\)
b. The fair price to play the game is \(\$4\)