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# Each of the Total Five Questions in a Multiple Choice Examination Has Four Choices, Only One of Which is Correct. a Student is Attempting to Guess the Answer. the Random Variable X is the Number of Questions Answered Correctly. What is the Probability that the Student Will Give Atleast One Correct Answer? - Mathematics and Statistics

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Each of the total five questions in a multiple choice examination has four choices, only one of which is correct. A student is attempting to guess the answer. The random variable x is the number of questions answered correctly. What is the probability that the student will give atleast one correct answer?

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#### Solution

Let X : number of question answered correctly out of 5.
p = P (correct answer)
p = 1/4
q = 1 - p = 3/4 and n = 5

X ~ B( n= 5,p =1/4)

The p.m.f of X is given as

p(X = x) = p(x) =""^5C_x(1/4)^x(3/4)^5-x

where x = 0, 1, 2, 3, 4, 5
Probability a student will get at least one correct answer

= P(X ≥ 1) = 1 - P(X < 1)
= 1 - P(X = 0)

=

1-""^5C_0(1/4)^0(3/4)^5

=

1-243/1024

=781/1024=0.7627

Concept: Probability Distribution of a Discrete Random Variable
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