Problem 3. Cereal Discrete Math Wizards consists of lumps made of granola and ra

Question

Problem 3. Cereal Discrete Math Wizards
consists of lumps made of granola and raisins shaped like littlenerds.
To boost sales, each box contains also a card with a major figurefrom
the history of Discrete Mathematics, like Gauss, Pascal, Aristotleor
Chebyshev. Altogether, there are 12 such major figures. Eachbox
contains a random card, one of 12 different kinds.







a)   
How many boxes, on the average, we will buy if we buy a box untilwe
collect all 12 different cards?







b)    How many boxes, on
the average, we will buy if we buy a box until we collect 10different
cards (i.e. until there are only 2 types that we do not have)?

Explanation / Answer

Second Probability = 11/12 Third Probability= 10/12 Fourth= 9/12 Fifth=8/12 Sixth= 7/12 Seventh= 6/12 Eighth= 5/12 Ninth= 4/12 Tenth= 3/12 Eleventh= 2/12 Twelfth= 1/12
Multiply all these probabilities together to get the answer.(I know there is an easier way but my calculator is archaic.) Probability is .0000537 or 0.0054%
To get only 10 cards, you need to exclude the last twoprobabilities. Probability is .003868 or 0.386%

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