Question

Assume that random guesses are made for ten multiple choice questions on a medical admissions​ test, so that there are n= 10 trials, each with a probability of success​ (correct) given by p= 0.20. Find the probability that the number x of correct answers is fewer than 3.

Answer 1

Given that ,

p = 0.20

1 - p = 1 - 0.20= 0.80

n = 10

Using binomial probability formula ,

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

P(X <3 ) = P(X=0) +P(X=1)+P(X=2)

= (10 C 0) * 0.200 * (0.80)10+(10 C 1) * 0.201 * (0.80)9+(10 C 2) * 0.202 * (0.80)8

probability =0.6778