Question

Jim Thorton's is a famous Canadian coffee franchise. Every year, Jim Thorton's holds a promotion where millions of promotional cups are produced and 10% of these cups contain a free prize hidden under the rim of the cup. Since the number of promotional cups is so massive, you can safely assume that the probability of purchasing a winning cup is independent of the number of winning cups that have already been sold. Over the course of this promotion, your group of friends obtain 200 cups, which you may assume is a random sample. What is the probability that your sample of cups has at least 30 winners?

Answer 1

We are given n = 200. The probability of a winning cup is p=10%=0.10

Let X be the number of winning cups out of 200. Then

X ~ Binomial(200,0.10)

We need to find the probability:

Now we will calculate it using two methods:

Method 1 - Accurate

We will use excel to calculate the exact probability:

=1-BINOM.DIST(29,200,0.1,TRUE)

=0.01632656593

Method 2 - Normal Approximation to binomial

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