Answer to Question #344875 in Statistics and Probability for Akshay

Question #344875

In the latest format of KBC, there are 5 questions. Like you all know, each question has 4 options and only one option is correct. However, in the new format, you get a chance to answer all 5 questions irrespective of the fact that you answer it right or wrong. What is the probability of getting 2 or 3 questions right?


1
Expert's answer
2022-06-06T05:48:54-0400

Let X=X= the number of right answers: XBin(n,p).X\sim Bin (n, p).

Given n=5,p=1/4=0.25,q=1p=0.75.n=5, p=1/4=0.25, q=1-p=0.75.


P(X=2 orX=3)=P(X=2)+P(X=3)P(X=2\ or X=3)=P(X=2)+P(X=3)

=(52)(0.25)2(0.75)52+(53)(0.25)3(0.75)53=\dbinom{5}{2}(0.25)^{2}(0.75)^{5-2}+\dbinom{5}{3}(0.25)^{3}(0.75)^{5-3}

=0.3515625=0.3515625

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