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4 April, 16:31

In 2012, Red Rose tea randomly began placing 1 of 12 English porcelain miniature figurines in a l00-bag box of the tea, selecting from 12 nautical figurines. On the average, how many boxes of tea must be pur - chased by a customer to obtain a complete collection consisting of the 12 nautical figurines?

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  1. 4 April, 16:58
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    n = 144 bags

    Step-by-step explanation:

    Given:-

    - English porcelain miniature figurines in total = 12

    - 1 figurine is to be placed in a 100-bag box

    Find:-

    On the average, how many boxes of tea must be pur-chased by a customer to obtain a complete collection consisting of the 12 nautical figurines?

    Solution:-

    - We will denote a random variable (X) as the number of figurines in (n) number of bags purchased.

    - The probability (p) of finding a figurine in a single bag is (success):

    p = 1 / 12

    - The random variable (X) can follow a binomial distribution with parameters n = number of bags purchased, and p = probability of selecting a bag with a figurine.

    X ~ B (n, 1/12)

    - The average number of bag "n" that need to be purchased to find all 12 figurines available:

    E (X) = 12

    n*p = 12

    n = 12 / p

    n = 12 / (1 / 12) = 12^2

    n = 144 bags

    - A total of average n = 144 bags need to be purchased to find all the 12 figurines.
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