Problem 42E

Refer to Exercise 3.41. What is the probability that a student answers at least ten questions correctly if

a for each question, the student can correctly eliminate one of the wrong answers and subsequently answers each of the questions with an independent random guess among the remaining answers?

b he can correctly eliminate two wrong answers for each question and randomly chooses from among the remaining answers?

Reference

A multiple-choice examination has 15 questions, each with five possible answers, only one of which is correct. Suppose that one of the students who takes the examination answers each of the questions with an independent random guess. What is the probability that he answers at least ten questions correctly?

Solution:

Step 1 of 3:

It is given that a multiple choice examination has 15 questions each with five possible answers out of which one is correct.

We have to find the probability that a student answers at least 10 questions correctly under the given conditions.