Question

Of the pupils in a school, 30% travel to school by bus. From a sample of 10 pupils chosen at random, what is the probability that more than 8 travel by bus?

Answer 1

`C_(10,9)(.3)^9(.7)^(1)+C_(10,10)(.3)^10(.7)^(0)~~0.00014`

Explanation:

We have a binomial probability. I like to start these kinds of questions with this relation:

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

We have `n=10, p=.3` and are looking at `8 < k <=10`:

`C_(10,9)(.3)^9(.7)^(1)+C_(10,10)(.3)^10(.7)^(0)~~0.00014`