Question

fan and medal !!
calculate the probability of randomly guessing the given number of correct anwsers on a 30 question multiple choice exam that has choices a,b,c,and d for each question
22.15
23.21

Answer 1

i think it is 22.15 but i am not 100% sure

Answer 2

For any given question, there is a \(\dfrac{1}{4}\) probability of guessing the correct answer, and so the probability of not guessing a question correctly is \(\dfrac{3}{4}\).

To guess any 22 of the 30 correctly, you compute the binomial probability,
\[P(X=22)=\binom{30}{22}\left(\frac{1}{4}\right)^{22}\left(\frac{3}{4}\right)^{8}\]
In general, to guess any \(k\) correct answers, the probability is given by
\[P(X=k)=\binom{30}{k}\left(\frac{1}{4}\right)^{k}\left(\frac{3}{4}\right)^{30-k}\]