A student is taking a multiple-choice quiz in which each question has four choic

Question

A student is taking a multiple-choice quiz in which each question has four 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 four balls (marked A, B, C, and D)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 five multiple-choice questions on the quiz. Complete parts (a) through (d) below. Round answers to four decimal places.

a.) What is the probability she will get five questions correct?

b.) What is the probability she will get at least four 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?

Explanation / Answer

Prob of getting one question correct is 0.25

a.

P(all correct ) = 0.25^5 = 0.00097

b.P(atleast 4 correct ) = P(4 correct) +P(all correct )

P(4 correct) = C(5,4) *(0.25^4)*(0.75) = 5*0.00292 = 0.0146

P(atleast 4 correct ) =0.01561

c.

P(all incorrect) = 0.75^5 = 0.2373

d.

P(no more than 2 correct) = P(all incorrect )+ P(prob 1 correct)+P(two correct)

=  0.2373 + C(5,1)*0.25*0.75^4+C(5,2)*0.25^2*0.75^3

=0.2373+5*(0.25)*(0.75^4)+10*(0.25^2)*(0.75^3) = 0.8965

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