prob. of getting exactly 4 correct on 20-Q multiple-choice

If a student randomly guesses at 20 multiple-choice questions, what is the probability that the student gets exactly four correct. Each question has four possible choices.

This is standard binomial proability.

\(\displaystyle \L\\C(n,k)p^{k}q^{n-k}\)

If chosen at random, since there are 4 choices, there is a 25% chance of answering each question correctly

\(\displaystyle \L\\C(20,4)(0.25)^{4}(0.75)^{16}\)

The parakeet problem works the same way.

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