Question

Lily really likes Smarties chocolate candies, which come in boxes of 40 pieces. However, Lily only keeps those boxes in which more than half of the candies are blue, her favourite colour (assume that the other possible colours of candies are red and yellow).

Lily wants to have a stock of 20 Smarties chocolate boxes that satisfy her colour restriction. What is the expected number of boxes she must purchase to get her needed “blue majority” Smarties chocolate boxes?

Assume that each piece of chocolate has an equal probability of being any of the three colours

Answer 1

As all the three colours are equally likely, the probability that a candy is blue is obtained here as: p = 1/3. Therefore the number of blue chocolates in a box of 40 chocolates here is modelled as:

Therefore the probability that more than 20 blue candies are there in a box is computed here as:

Now the expected value of boxes that are to be bought so that we get 20 boxes of the required kind of boxes is computed here as:

= 20/ Probability of getting a required type of box

This is the required probability here.