Question

2.10 Guessing on an exam: In a multiple choice exam, there are 7 questions and 4 choices for each question (a, b, c, d). Nancy has not studied for the exam at all and decides to randomly guess the answers. What is the probability that:
(please round all answers to four decimal places)


a) the first question she gets right is question number 3?
b) she gets all of the questions right?
c) she gets at least one question right?

Answer 1

In a multiple-choice exam, there are 7 questions and 4 choices for each question (a, b, c, d).

n = 7 and p = 0.25 and q = 1 - p = 0.75.

a.

The probability that the first question she gets right is question number 3 is q.q.p = 0.75*0.75*0.25 = 0.140625.

b.

The probability that she gets all of the questions right is p^7 = 0.25^7 = 6.103516e-05.

c.

The probability that she gets at least one question right is P(X 1) i.e

This implies that

Pr(X≥1) = 0.8665.