A student is taking a multiple-choice exam in which each question has five choices. Assuming that she has no knowledge of the correct answers to any of the questions, she has decided on a strategy in which she will place five balls (marked A, B, C, D, and E) into a box. She randomly selects one ball for each question and replaces the ball in the box. The marking on the ball will determine her answer to the question. There are four multiple-choice questions on the exam.

a) What is the probability that she will get four questions correct?

b) What is the probability that she will get at least three questions correct?

c) What is the probability that she will get no questions? correct?

d) What is the probability that she will get no more than two questions correct?

a) The answer is 0.0064

b) The answer is 0.05792

c) The answer is: 0.32768

d) The answer is: 0.94208

Explanation:

We have:

* Probability of one answer correct = 1/5 = 0.2

* Probability of one answer incorrect = 1 - 0.2 = 0.8

Probability of x answer is correct = 0.2^x * 0.8^ (5-x) * c (5, x)

So:

a) The probability four answer is correct = 0.2^4 * 0.8^1 * c (5,4) = 0.0064

b) The probability she will get at least three questions correct = The probability four answer is correct + probability three answer is correct + probability five answer is correct = 0.0064 + 0.2^3 * 0.8^2 * c (5,3) + 0.2^5 * 0.8^0 * c (5,5) = 0.05792

c) The probability that she will get no questions correct = 0.2^0 * 0.8^5 * c (5,0) = 0.32768

d) The probability that she will get no more than two questions correct = 1 - The probability she will get at least three questions correct = 1 - 0.05792 = 0.94208.