4 Balls with numbers from 1 to 100 are in a bag for you to p

4) Balls with numbers from 1 to 100 are in a bag for you to pick one at random. If the number is even you win $2, if you pick number 13 you win $50, if you pick 7 or 11 you win $20, and if you pick number 99 you win $10. What is the fair price to charge to play this game?

Solution

The fair price to charge to play this game will be the average expected win reward; Since the reward of victory varies from number to number we need to calculate the average reward considering a weighted average mean. So, Reward R=
1/100 ( 2 +2 + 2 + 2 .....50 times 2) (this is reward 2$ for each even number)
+ 1/100 ( 50) (this is 50$ reward for the ball numbered 13)
+ 1/100 ( 20+20) (this is 20$ reward each for the ball numbered 7 or 11)
+ 1/100 ( 10) ( this is 10$ reward for picking ball numbered 99)
The sum is = 1/100 ( 50*2 + 50+40+10) = 1/100 ( 200) = 2$

Thus, the fair price charged to play this game must be 2$