Question: A cereal company puts a plastic bear in each box of cereal. Every fifth bear is red. If you have three red bears, you get

A cereal company puts a plastic bear in each box of cereal. Every fifth bear is red.

If you have three red bears, you get a free box of the cereal. If you decide to keep buying this cereal until you get one box free, how many boxes would you expect to buy before getting a free one? [Hint: Represent the answer as E(X1 + X2 + X3), where Xi is the number of boxes you buy after getting the (i − 1)st red bear and until getting ith red bear.]

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