SOLUTION: Suppose there are 6 prizes hidden in the boxes of a particular cereal brand. How many boxes of the cereal would you expect to buy before collected all 6 prizes?

Question 65255: Suppose there are 6 prizes hidden in the boxes of a particular cereal brand. How many boxes of the cereal would you expect to buy before collected all 6 prizes?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Seems to me you need to know the probability a particular box has
the prize or prizes.
If you simulate the experiment you proceed as follows:
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Let's say you simulate the experiment 25 times and
get results like
7 rolls to get the 6 prizes: 5 times
8 rolls to get the 6 prizes: 8 times
9 rolls to get the 6 prizes; 6 times
10 rolls to get the 6 prizes: 3 times
11 rolls to get the 6 prizes: 3 times
Then:
P(7 boxes to get the 6 prizes )=5/25
P(8 boxes)=8/25
P(9 boxes)=6/25
P(10 boxes)=3/25
P(11 boxes)=3/25
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Then, expected number of boxes = 7*5/25 + 8*8/25+9*6/25+10*3/25+11*3/25
=[35+64+54+30+33]/25
=216/25
=8.64 boxes
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Hope this helps.
Cheers,
Stan H.

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