A student is taking a multiple-choice exam in which each question has two choice

Question

A student is taking a multiple-choice exam in which each question has two 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 two balls (marked Upper A and Upper B) 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 eight multiple-choice questions on the exam.

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

Explanation / Answer

d) P(correct answer), p = 0.5

P(wrong answer), q = 0.5

Number of questions, n = 8

Binomial distribution: P(X) = nCx px qn-x

P(she will get no more than two questions correct) = P(0) + P(1) + P(2)

= 0.58 + 8C1x0.5x0.57 + 8C2x0.52x0.56

= 0.1445

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