Question

In a box there are four prizes that are worth $40, three prizes worth $100, and one prize worth $2000. A player will reach into the box and draw one of the prizes at random. What is the fair price for this game? Round your answer to the nearest hundredth, and do not include a $ sign or the word "dollars" in your response.

Answer 1

Let x be the fair price for this game.

From the given data, the following Table is calculated:

Event	Value (x)	Probability (p)	x.p
Drawing the prize of $40	40 - x	4/8 = 0.5	(40 - x) X 0.5 = 20 - 0.5 x
Drawing the prize of $100	100 - x	3/8 = 0.375	(100 - x) X 0.375 = 37.5 - 0.375 x
Drawing the prize of $2000	2000 - x	1/8 = 0.125	(2000 - x) X 0.125 = 250 - 0.125x
Total = Expected Value of the game			307.5 - x

For fair price for the game,

Expected Value of the gamemust be 0.

Thus, we get:

307.5 - x = 0

So,

x = the fair price for this game.= 307.50

So,

Answer is:

307.50