SOLUTION: A grab bag contains 12 packages worth 80 cents apiece, 15 packages worth 40 cents apiece, and 25 packages worth 30 cents apiece. Is it worthwhile to pay 50 cents for the priviled

Click here to see ALL problems on Probability-and-statistics

Question 717692: A grab bag contains 12 packages worth 80 cents apiece, 15 packages worth 40 cents apiece, and 25 packages worth 30 cents apiece. Is it worthwhile to pay 50 cents for the priviledge of picking one of the packages at random? Why or why not?
Answer by DrBeeee(684) (Show Source):
You can put this solution on YOUR website!
Calculate the expected value of the package selected at random. This is given by the probability of selecting a particular package multiplied by it's value. There are 12+15+25 = 52 total packages. The probability of selecting an 80 cent package is 12/52. It's expected value is then 12/52*80 or about 18.5 cents. Add up all three types and get
(1) Expected value = (12*80 + 15*40 + 25*30)/52 or
(2) Expected value = 44.42 cents
It is NOT worthwhile to pay 50 cents to pick a package because my expected return is 44.42 cents. In the "long" run you'd lose more than 5 cents per selection.