Question

Asked Oct 16, 2019

In 2016, Red Rose tea randomly began placing one of ten English porcelain miniature figurines in a l00-bag box of the tea, selecting from ten figurines in the American Heritage Series. (a) On the average, how many boxes of tea must be pur-chased by a customer to obtain a complete collection consisting of the ten different figurines? (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?

Step 1

Since the first box contains any one miniature figurine, therefore probability of getting any one miniature figurine in the first box is 10/10 = 1. Similarly probabilities of getting 2^{nd}, 3^{rd},…10^{th} miniature figurines in 2^{nd}, 3^{rd},…10^{th} boxes are 9/10, 8/10,…1/10.

Step 2

Since the above probabilities are geometric probabilities, the expected number of boxes to be purchased to get 1st, 2nd, 3rd,…10th miniature figurines are 1, 10/9, 10/8,…10/1.

There...

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