SOLUTION: A multiple choice exam has 60 questions . Each question has 4 possible answers and only 1 answer out of the 4 possible answers is correct . To receive an A grade , one must answer

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Question 1102436: A multiple choice exam has 60 questions . Each question has 4 possible answers and only 1 answer out of the 4 possible answers is correct . To receive an A grade , one must answer 95% and above of the question correctly. We know that 54 questions were answered correctly . What is the probability of receiving an A grade ?
A . 0.169
b. 0.466
c. 0.500
d. 0.743
Answer : A
Answer by natolino_2017(77) (Show Source):
You can put this solution on YOUR website!
95% of 60 questions means at least 57 questions. As you already know that you have 54 right answers. You must have at least 3 right answer from the missing 6.
Let p the probability of get one of them correctly.
p=1/4.
Let X~Binnomial(n=6,p=1/4)
Where X is the number of right answers between the 6 questions.
P(X>=3)= 1 - P (X <3) = 1- P(X=0 U X=1 U X=2)
=1-(P(X=0)+P(X=1)+P(X=2))=1-(6C0(1/4)^0(3/4)^6 + 6C1(1/4)^1(3/4)^5 +6C2(1/4)^2(3/4)^4)=1-(3^6+2(3^6)+5(3^5))/4^6= 0.1694.
So the right choice is A.
#Natolino