A multiple-choice test contains 25 questions, each with five answers. Assume that a student just guesses on each question. What is the probability that the student answers more than 10 questions correctly

the probability that the student answers more than 10 questions correctly is 0.01733

Step-by-step explanation:

This is a binomial distribution problem.

Probability of a correct answer, p = 1/5 = 0.2

Probability of an incorrect answer, q = 4/5 = 0.8

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

But for the probability that the student answers more than 10 questions correctly

P(X ≥ 10) = 1 - P(X < 10)

But P(X < 10) will be the sum of all the probabilities from 0 to 1, to 2, to 3, up till 9.

P(X < 10) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9)

Computing each of this using the formula

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

where n = 25

p = 0.2

q = 0.8

x = 0,1,2,3,4,5,6,7,8,9

P(X < 10) = 0.9827

P(X ≥ 10) = 1 - P(X < 10) = 1 - 0.9827 = 0.01733