One of four different prizes was randomly put into each box of a cereal. If a family decided to buy this cereal until it obtained at least one of each of the four different prizes, what is the expected number of boxes of cereal that must be purchased?

Answer :

Step 1 of 1:

From the given information one of four different prizes was randomly put into each box of a cereal.

If a family decided to buy this cereal until it obtained at least one of each of the four different prizes.

Now we have to find the expected number of boxes of cereal that must be purchased.

One prize in each box,then there is a prize in the first box.

Then the expected value of is

: number of trials that needed to get the prize 2.

Here p = 3/4

Then the expected value of is

: number of trials that needed to get the prize 3.

Here p = 2/4

Then the expected value of is

and

: number of trials that needed to get the prize 4.

Here p = 1/4

Then the expected value of is

Then we are adding all expected value to find the number of boxes of cereal.

So

Substitute all the values.

Therefore the expected number of boxes of cereal that must be purchased is .