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.

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