Discrete Distribution/Geometric Probability

AI Thread Summary
The discussion focuses on calculating the expected number of tea boxes needed to collect all miniature animals from Red Rose tea. For part a, the average number of boxes required is derived using the formula μ = r * (1/p), with the result being 7381/252. Participants suggest utilizing the "coupon collector's problem" for better understanding and solutions. The n * Hn method, involving the number of items and the Harmonic series, is recommended for solving these types of problems. Overall, the conversation emphasizes mathematical approaches to discrete distributions and geometric probability in practical scenarios.
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Homework Statement



In 2006, Red Rose tea randomly began placing 1 of 10 English porcelain miniature animals in a 100-bag box of the tea, selecting from 10 "Pet Shop Friends."

a) On the average, how many boxes of tea must be purchased by a customer to obtain a complete collection consisting of 10 different animals?

b) If the customer uses one tea bag per day, how long can a customer expect to take, on the average, to obtain a complete collection?

c) From 2002 to 2006, the figurines were part of the Noah's Ark Animal Series, which contains 15 pieces. Assume again that these figurines were selected randomly. How many boxes of tea would have had to be purchased, on the average, to obtain the complete collection?

Homework Equations



μ = r * (1/p), σ2= q/p2, σ = (1-q)/p

The Attempt at a Solution



Answer for part a) = 7381/252

I'm not sure how to set this up. There are solutions to the problem but they seem extremely long and did not follow anything from the text.
 
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Google the "coupon collector's problem".

RGV
 
Ray Vickson said:
Google the "coupon collector's problem".

RGV

Thanks.

Looks like the best way to going about these problems are using the n * Hn method (number of items times the Harmonic series)
 
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