A student is taking a multiple choice exam in which each question has five choic

Question

A student is taking a multiple choice exam in which each question has five choices. Assume that the student 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, D, and E into a box. The student then draws a ball for each question and after recording the mark on the ball as the answer, returns the ball to the box. The test consists of five questions.

a.What is the probability the student gets no questions correct?   

b.What is the probability the student gets no more than two questions correct?

Explanation / Answer

P(correct) = 1/5 = 0.2 =>P(not correct) = 1 - 0.2 = 0.8. Given there are five questions

(a) P(no question correct) = 0.8*0.8*0.8*0.8*0.8 = 0.3277.

(b) P(no more than two correct) = P(0 correct)+P(1 correct)+P(2 correct)

= (5C0*(0.2)0*(0.8)5)+(5C1*(0.2)1*(0.8)4)+(5C2*(0.2)2*(0.8)3) = 0.3277+0.4096+0.2048 = 0.9421

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