Question

a student answers all 48 questions on a mulitple choice test by guessing. each question has 4 possible answers only one is correct. find the probability that the student gets exactly 15 correct

Answer 1

P(of 1 right question) =1/4 =0.25 & P(of wrong question) = 3/4 =0.75

He has got 48 questions & answered 15 right questions==> Here we have to use the binomial probability ==>nCr (p)^r . q^(n-r)
p=0.25 & & q=1-r ==>q=0.75

₄₈C₁₅ =(0.25)¹⁵.(0.75)³³ =0.0767 or 7.67%