Question

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

There are a total of n=7 questions, each of which has 4 options. Out of these 4 options, only one of them is correct. Thus, the probability of guessing a question correctly is and similarly the probability that the question is incorrect is .

(a)

The required probability in this case is to determine the chances that the first question she gets right is the question number 3. This implies:

Required Probability = Probability that first two questions are incorrect × Probability that the next question is correct

That is,

(b)

The Required probability in this case is to determine the chances that she attempts all the questions correctly, that is:

Required Probability = Probability that first question is correct × Probability that the second question is correct × ... × Probability that the seventh question is correct

Mathematically,

(c)

In this case the probability of obtaining atleast one question correct needs to be determined.

Required Probability = Probability that atleast one question is correct = 1 - Probability that no question is correct

Mathematically,