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A professor gives students a pop quiz with 5 true or false questions. Eighty percent of the students are well-prepared for the pop quiz, but twenty percent are not. Students who are prepared have a 85% chance of answering each question correctly, but the students who are unprepared simply randomly guess and have a 50% chance. Find the probability that a student was well-prepared under the following scenarios:

(a) Answered 1 correctly

(b) Answered 2 correctly

(c) Answered 3 correctly

(d) Answered 4 correctly

 Feb 29, 2020
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(1) The probability is 3/17.

 Mar 3, 2020

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