Entered Answer Preview Result 0.421875 0.421875 correct 13 27 0.999194 incorrect
ID: 3042749 • Letter: E
Question
Entered Answer Preview Result 0.421875 0.421875 correct 13 27 0.999194 incorrect At least one of the answers above is NOT correct. 1 point) For this question, you need at least 6 decimal places. An exact answer (fractions) is recommended on both parts, especially the first part since it will be used for the second question Baumgartner, Prosser, and Crowell are grading 13 calculus exams on which there is a series of 3 multiple choice questions. Each question has 4 answer choices. Crowell says, "I bet we should expect at least three exams in which no answer is correct if everyone is just guessing." First, what is the probability that a student gets no answer correct on the 3 multiple choice questions if he or she guesses randomly with no bias? 0.421875 What is the probability that there are at least three exams with no answer correct if all 13 students are guessing? Hint: use your answer from part (a) as the probability of success here. Your trials are the exams (students) now, and we want at least three successes You may need to leave your answer as a sum of powers of fractions. (1-(1-27/64)A13)Explanation / Answer
Answer to the question is as follows:
So, no answer correct on the 3 multiple choice quations if there' no bias
= (3/4)^3
= .421875
P(X>=3) = 1- P(X=0,1,2) , where P(X=k) is the probability that k students answered none correctly
= 1 -[ (13C0 (.421875)^0 *(1-.421875)^13 )+(13C0 (.421875)^0 *(1-.421875)^13)+(13C0 (.421875)^0 *(1-.421875)^13 )]
= 1-0.041924
= 0.958076
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