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?

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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.

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

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