Answer to Question #344875 in Statistics and Probability for Akshay

Question

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?

Answer 1

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

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

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

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

$$=0.3515625$$