An unprepared student is about to take his first test of the semester. He is tol

Question

An unprepared student is about to take his first test of the semester. He is told that his test will be composed of 15 multiple choice questions, each with 4 possible answers, only one of which is correct.

1.What is the probability that the unprepared student randomly guesses at the correct response on ONE of the questions and gets the question correct?

2.What is the probability that the unprepared student randomly guesses at the correct response on ONE of the questions and gets the question wrong?

3.What is the probability that the student guesses at all 15 questions and gets at least one questions correct?

Explanation / Answer

1) probability that the unprepared student randomly guesses at the correct response on ONE of the questions and gets the question correct =1/4 =0.25 ((as there is 1 correct answer out of 4)

2)probability that the unprepared student randomly guesses at the correct response on ONE of the questions and gets the question wrong =3/4 =0.75 (as there are 3 wrong answers out of 4)

3) P( gets at least one correct )=1-P(get all wrong) =1-(3/4)15 =0.986637

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