Question

In a box there a total of four prizes: Two of them are worth $4, a single prize worth $17, and a single prize worth $225. A player will reach into the box and draw one of the prizes at random. What is the fair price for this game?State your answer in terms of dollars rounded to the nearest cent (hundredth).

Answer 1

Answer:

$62.50

Explanation:

In the box:

The total number of prizes = 4

• The number of prizes worth $4 = 2

,

• The number of prizes worth $17 = 1

,

• The number of prizes worth $225= 1

Let X be a random variable representing the prize amount.

• X=4,17,225

First, we determine the probability of selecting each of the prizes.

$\begin{gathered} \text{P(X= \ }4)=\frac{2}{4} \\ \text{P(X=\ 17})=\frac{1}{4} \\ \text{P(X=\ 225})=\frac{1}{4} \end{gathered}$

Next, we calculate the expected value for the game.

We calculate the expected value by multiplying the probability of each prize by the prize and adding them up.

$\begin{gathered} \text{Expected Value}=\sum xP(x) \\ \text{=(}\ 4\times\frac{2}{4})+\text{(}\ 17\times\frac{1}{4})+\text{(}\ 225\times\frac{1}{4})\text{=}\ 2+\ 4.25+\ 56.25 \\ =\ 62.50 \end{gathered}$

The expected value is $62.50.

Therefore, it is reasonable to set the fair price for this game at $62.50.