Five different CDROM games Garble Trapster Zoom Bungie blas

Five different CD-ROM games, Garble, Trapster, Zoom!, Bungie & blast\'Em, are offered as a promotion by sugarush cereals. One game is randomly included

With each box of cereal.

a) determine the pobability of getting all 5 games if 12 boxes are purchased.

b) explain the steps in your solutions.

c) discuss any assumptions that you make in your analysis

Solution

First let\'s assume that all the games are uniformly distributed i.e. any game is equaly likely to be found in a random box of cereal. That means that probability of getting any of the five games in a randomly selected box is `p=1/5` (because there are 5 games).

Since probability that a game is in a random box is `p=1/5` then probability that game is not in a random box is `q=1-1/5=4/5`. Now since our choosing of boxes is mutally independent probability that a game is not found in any of 12 boxes is `(4/5)^12 approx 0.0687` which means that probability of getting all 5 games from 12 boxes is approximately `1-0.0687=0,9313`.