Question

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.

Answer 1

Answer:

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,

=$P(X=3) = 0.08192$

(b) being correct on four questions,

= $P(X=4) = 0.01536$

(c) being correct on all six questions

=$P(x=6) = 0.000064$