202 CHAPTER 5 Discrete Probability Distributions 5.23 A student is taking a mult

Question

202 CHAPTER 5 Discrete Probability Distributions 5.23 A student is taking a multiple-choice exam in which each question has four choices. Assume that the student has no knowl- edge of the correct answers to any of the questions. She has de- cided 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 exam. What is the probability that she will get a. five questions correct? b. at least four questions correct? c, no questions correct? d. no more than two questions correct?

Explanation / Answer

3. Fair tossed 3 times

a. 5 Qn correct = ?

= 5C5 ( 1/4)^5 (3/4)^0 = 0.0039

b. P(at least 4 Qn correct)?
= P( 4 correct or 5 correct)
= 5C4 ( 1/4)^4 (3/4)^1 +5C5 ( 1/4)^5 (3/4)^0
= 0.0156

c. P(no qn correct) = 5C0(.25^0)(.75^5) = 0.2373

d. P(no more than 2 Qn correct) = P(X=0, 1,2) = 5C50(.25^0)(.75^5)+5C1(.25^1)(.75^4)+5C2(.25^2)(.75^3) = 0.8965

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