in the textbook. Number each of the lfiless otherwise specified. 10 Q83 Binomial
ID: 3283097 • Letter: I
Question
in the textbook. Number each of the lfiless otherwise specified. 10 Q83 Binomial : Multiple Choice Exam Pages 210-213 e Suppose on a multiple choice exam there are 9 questions and each question has exactly 5 possible choices If someorn Someone randomly guesses the answer for each question, what is the probability of getting exactly 4 ques- tions incorrect. Assume that you answer cach question and that each question has exactly 1 correct answer, and that the answer to any question is independent of the answer to any other question. Express your final answer as a decimal number rounded to 4 significant digits. 6 pointsExplanation / Answer
SOL)
Assuming each the answer to each question is independently chosen, the answer should be the number of ways we can order 6 correct answers and 3 incorrect answers.
A correct answer has a probability of 1/5 for an individual question, and 4/5 for an incorrect answer.
There are C(9,3) ways to select the 3 correct answers out of 9 questions. So the final probability should be
C(9,3)* (1/5)^6* (4/5)^3
=84*0.000064*0.032 = 0.00017203
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