Discrete Distribution/Geometric Probability

[trojansc82]

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.

 

[Ray Vickson]

Google the "coupon collector's problem".

RGV

 

[trojansc82]

Google the "coupon collector's problem".

RGV

Thanks.

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