Question

A quiz consists of 20 multiple-choice questions, each with 5 possible answers. For someone who makes random guesses for all of the answers, find the probability of passing if the minimum passing grade is 50 %. Enter your answer in decimal form accurate to six decimal places.

Answer 1

0.00259

Explanation:

Probability, p of making the correct guess ; 1 / 5 = 0.2

Passing grade = 50% ; 50% * 20 = 0.5 * 20 = 10

q = probability of not passing ;

q = 1 - p = 1 - 0.2 = 0.8

Using the binomial distribution formula :

P(x >=x) = nCx * p^x * (1 - p)^(n - x)

P(x >= 10) = p(x = 10) + p(x = 11)+... + p(x = 20)

P(x >= 10) = 10C20 * 0.2^10 * 0.8^10

P(x >=) 0.00259