A cash prize is randomly placed into certain cereal boxes that sell for $5. A $1 prize is placed in 10% of cereal boxes, a $5 prize is placed in 5% of cereal boxes, while 10% of boxes receive a $20 prize. The other boxes do not receive any cash prizes. What is the expected value of the cash prizes if you include the cost of purchasing the cereal in your calculations?

-2.65 usd

Step-by-step explanation:

1. Note that  10%= probability 0.1  5%= 0.05 .

Lets find the average prize value :

1 usd *P(1 uzd)+5usd *P(5usd)+20,usd*P(20usd)=

= 1*0.1+5*0.05+20*0.1=2.35 USD is a value average prize brutto.

However for 1 turn the player has to pay 5 USD.

That means the net value is 2.35-5=-2.65 USD

Actually it means that every turn the player loses 2.65 USD averagly.