Document1 Word nces Mailings Review View Aa- .a- 13-E-1111 NorrmalTNo Tell me wh

Question

Document1 Word nces Mailings Review View Aa- .a- 13-E-1111 NorrmalTNo Tell me what you want to do Spac... Heading 1 Heading 2 Title Paragraph Styles A student is taking a multiple-choice exam 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 Upper A comma Upper B comma Upper C comma and Upper DA, 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. Complete parts (a) through (d) below. a. What is the probability that she will get five questions correct? b. What is the probability that 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 co tD e@ «J#

Explanation / Answer

n = 5

P(correct) = 1/4 = 0.25

A) P(X = 5) = 5C5 * (0.25)^5 * (0.75)^0 = 0.0010

B) P(X > 4) = P (X = 4) + P (X = 5)

= 5C4 * (0.25)^4 * (0.75)^1 + 5C5 * (0.25)^5 * (0.75)^0 = 0.0156

C) P(X = 0 ) = 5C0 * (0.25)^0 * (0.75)^5 = 0.2373

D) P(X < 2) = P(X = 0) + P (X = 1) + P( X = 2)

= 5C0 * (0.25)^0 * (0.75)^5 + 5C1 * (0.25)^1 * (0.75)^4 + 5C2 * (0.25)^2 * (0.75)^3 = 0.8965

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