Question

Example: For the multiple choice test example (10 questions, each with 8 choices), what is the probability that the person gets 2 or 3 questions correct?

Answer 1

X~ binomial (n,p)  

Where n = 10, p = 1/8

Binomial probability distribution is

P(X) = ⁿC_x p^x (1-p)^n-x

So,

P(X = 2 or 3) = P( X = 2) + p( x = 3)

= ¹⁰C₂ (1/8)² (7/8)⁸+¹⁰C₃ (1/8)³ (7/8)⁷

= 0.3336