Question

Q3) A multiple choice test contains 25 questions each with four answers. Assume a student just guess on each question.

i. What is the expected number of the correct answers?

ii. What is the probability that the student answers more than 20 questions?

Answer 1

Question 3

A multiple choice test contains 25 questions each with 4 answers.

A student guesses on each question.

Now, as 1 answer is correct out of 4, so the probability that a student guesses rightly, is 1/4, ie. 0.25.

So, if X be the random variable denoting the number of correct questions out of 25, then X follows binomial distribution with parameters n = 25 and p = 0.25.

Question i

The expected number of correct answers is

Question ii

We have to find the chance that the student answers more than 20 questions correctly.

Now, the PMF of X is given by

Where, i can take integer values from 0 to 25.

So, we have to find

By calculating, it becomes a little less than 0.000001.