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?
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)
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