Question

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?

Answer 1

Answer:

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.