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

Question

A student is taking a multiple-choice test 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 BA and 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 four multiple-choice questions on the test.

What is the probability she will get four correct?

What is the probability she will get three correct?

What is the probability she will get two correct?

What is the probability she will get one correct?

What is the probability she will get zero correct?

Explanation / Answer

For any question,

P(Correct) = P(Incorrect) = 1/2

Hence,

a) P(X = 4) = (1/2)4 = 1/16 = 0.0625

b) P(X = 3) = 4*(1/2)3*(1/2) = 4/16 = 0.25

c) P(X = 2) = 6*(1/2)2*(1/2)2 = 6/16 = 0.375

d) P(X = 1) = 4*(1/2)*(1/2)3 = 4/16 = 0.25

e) P(X = 0) = (1/2)4 = 1/16 = 0.0625

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