Question

You have a 5-question multiple-choice test. Each question has four choices. You don’t know any of the answers. What is the experimental probability that you will guess exactly three out of five questions correctly?

Answer 1

As you know, the probability of answering k out of n questions correctly, given P(correct) = p, is

nCk * p^k * (1-p)^(n-k)

So, since you have
n=5
k=3
p=1/5

p(3 of 5) is 5C3 * (1/5)^3 * (4/5)^2 = 32/625

That is the theoretical probability. For experimental, you'd need to run several trials, and see how many times you got 3 of 5 correct.

Answer 2

oops. my bad. That would be 1/4 and 3/4, not 1/5 and 4/5