On a six-question multiple-choice test there are five possible answers for each question, of which one is correct and four are incorrect. If a student guesses randomly, find the probability of (a) being correct on three questions, (b) being correct on four questions, (c) being correct on all six questions.

Step-by-step explanation:

given that on a six-question multiple-choice test there are five possible answers for each question, of which one is correct and four are incorrect

By mere guessing probability for choosing correct answer = p = 0.2

also each question is independent of the other

Hence if X is the number of correct questions then

X is binomial with p = 0.2 and n = 6

a) being correct on three questions,

=

(b) being correct on four questions,

=

(c) being correct on all six questions

=