Question

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

Answer 1

Answer:

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