Question

From experience, the manager of Kramer's Book Mart knows that 60% of the people who are browsing in the store will make a purchase. What is the probability that among ten people who are browsing in the store, at least three will make a purchase?

Answer 1

`~~0.98771`

Explanation:

This is a binomial probability question. The general form is:

`sum_(k=0)^(n)C_(n,k)(p)^k(1-p)^(n-k)=1`

or in other words, the sum of all the possible results from a given population (`n`) from all the trials (`k`) with a set probability (`p`) will sum to 1.

Here, we have `n=10` and `p=0.6`.

We can sum up for `3<=k<=10` or we can subtract `0<=k<=2` from 1 to find the probability:

`1-(C_(10,0)(.6)^0(.4)^(10)+C_(10,1)(.6)^1(.4)^(9)+C_(10,2)(.6)^2(.4)^(8))~~1-0.01229~~0.98771`