Question

In a box there are two prizes that are worth $4, a single prize worth $20, and a single prize worth $200. 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

57

Explanation:

The player has a 1/4 chance of drawing any of the 4 prizes. This means that the probability of drawing a prize of $4 is 1/2 because there are 2 prizes worth of $4. The probability of drawing a prize of $20 is 1/4 and the probability of drawing a prize of $200 is also 1/4. To find the fair price of the game, we have to calculate the expected value that the player will gain. This can be obtained by multiplying any possible value of a price for the probability of drawing a prize of that value and adding all the obtained values togueter. Thus, the fair price of the game is

`4 * (1)/(2) + 20 * (1)/(4) + 200 * (1)/(4) = 57`