Question

Assume that random guesses are made for 12 multiple choice questions on a medical admissions​ test, so that there are n= 12 trials, each with a probability of success​ (correct) given by p= 0.25. Find the probability that the number x of correct answers is fewer than 6.

Answer 1

Given that ,

p = 0.25

1 - p = 1 - 0.25= 0.75

n = 12

Using binomial probability formula ,

P(X = x) = (n C x) * px * (1 - p)n - x

P(X <6) = P(X=0) +P(X=1)+P(X=2)+P(X=3)+P(X=4)=+P(X=5)

= (12 C 0) * 0.250 * (0.75)12+(12 C 1) * 0.251 * (0.75)11+(12 C 2) * 0.252 * (0.75)10+(12 C 3) * 0.253 * (0.75)9+(12 C 4) * 0.254 * (0.75)8+(12 C 5) * 0.255 * (0.75)7

probability =0.9456