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 20 multiple choice questions, each with 4 possible answers, only one of which is correct. a. What is the probability that the unprepared student randomly guesses at the correct response on ONE of the questions and gets the question correct? b. What is the probability that the unprepared student randomly guesses at the correct response on ONE of the questions and gets the question wrong? c. What is the probability that the student guesses at all 20 questions and gets at least one questions correct?

Explanation / Answer

a.
when student pick any one of the question and guess randomly for correct
will be = p(success) = 1/ 4 = 0.25
b.
a.
when student pick any one of the question and guess randomly for failure
will be = 1 - p(success) = 1 - 1/ 4 = 0.75
c.
Binomial Distribution
PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

P( X < 1) = P(X=0) +   
= ( 20 0 ) * 0.25^0 * ( 1- 0.25 ) ^20   
= 0.0032

P( X > = 1 ) = 1 - P( X < 1) = 0.9968

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