Question

A test consists of nine true/false questions. A student who forgot to study guesses rendomly on every question. What is the probability that the student answers at least two questions correctly?

Answer 1

`~~0.9805`

Explanation:

This is a binomial probability question.

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

We have `n=9, p=.5`, and we're interested in `k>=2`. We could work this to sum up all the `k` terms greater than or equal to 2, or we can find `k=0, 1` and subtract that sum from 1. That second way is far less work, so I'll do that:

`1-C_(9,0)(.5)^0(.5)^(9)-C_(9,1)(.5)^1(.5)^(8)~~0.9805`