# Five different CD-ROM games, Garble, Trapster, Zoom!, Bungie & blast'Em, are offered as a promotion by sugarush cereals. One game is randomly includedWith each box of cereal. a) determine the...

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

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### 1 Answer

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`.