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
