Suppose that you are taking a multiple-choice exam with six questions, each has four choices, and one of them is correct. Because you have no more time left, you cannot read the question and you decide to select your choices at random for each question. Assuming this is a binomial experiment, calculate the binomial probability of obtaining exactly one correct answer.

a. 0.297

b. 0.178

c. 0.356

d. 0.132

Answer: c. 0.356

Step-by-step explanation:

In binomial distribution, the probability of success does not change. Since each question has four choices and only one of them is correct, the probability of selecting a correct answer is 1/4 = 0.25. This is the probability of success, p. The probability of failure, q is 1 - p = 1 - 0.25 = 0.75

Total number of questions is 6. It means that the sample size, n is 6

We would determine the probability of obtaining exactly one correct answer, P (x = 1) by using the binomial distribution calculator. Therefore,

P (x = 1) = 0.356