Question

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.
b) the fair price to play the game.
a) the expectation is $1.00
(type an integer or a decimal rounded to the nearest cent.)
b) the fair price is $□
(type an integer or a decimal rounded to the nearest cent.)

Explanation:

Step1: Calculate the expectation

The spinner is divided into 4 equal - parts. The probability of landing on each part \(P=\frac{1}{4}\).
The amounts are \(x_1 = 1\), \(x_2=4\), \(x_3 = 10\), \(x_4 = 1\).
The formula for expectation \(E(X)=\sum_{i = 1}^{n}x_iP(x_i)\)

$$
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$$

Since it costs \(C = 3\) to play the game, the net - expectation \(E=E(X)-C\)

$$E = 4-3=1$$

Step2: Determine the fair price

The fair price to play the game is equal to the expected value of the game without considering the cost.
The expected value of the amounts on the spinner \(E(X) = 4\) (calculated above). So the fair price to play the game is the expected value of the amounts on the spinner.

Answer:

a) The expectation of a person who plays the game is \(\$1.00\)
b) The fair price to play the game is \(\$4.00\)