Question

What is the probability of Donny getting a passing score?

A Precalculus test contains 10 multiple choice questions. Each question has four answers to select from of which, only one is correct. If Donny has not studied for the exam and answers the questions randomly, what is the probability that he will get a passing score? (7/10)

Answer 1

`~~0.0035`

Explanation:

We can solve this using binomial probability. The relation I like to start with is:

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

We have `n=10, p=0.25` and are looking at `7<=k<=10`:

`C_(10,7)(0.25)^7(0.75)^3+C_(10,8)(0.25)^8(0.75)^2+C_(10,9)(0.25)^9(0.75)^1+C_(10,10)(0.25)^10(0.75)^0~~0.0035`