Question

. If a student is randomly choosing the answer to each of ten true-false questions in a test, what is the probability that he will have at most one incorrect answer (express the answer with four decimal places)

Answer 1

0.0107

Explanation:

Given that:

Probability of success in choosing a true - false answer :

(Number of correct answers / number of options)

= 1/2 ; p = 0.5

Number of questions = number of trials, n = 10

Probability of having atmost one incorrect answer :

p(incorrect answer) = 0.5

P(x ≤ 1) = p(0) + p(1)

Using binomial distribution formula :

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

When x = 0

P(x = 0) = 10C0 * 0.5^0 * 0.5^10

P(x = 0) = 1 * 1 * 0.0009765625

P(x = 0) = 0.0009765625

When x = 1

P(x = 1) = 10C1 * 0.5^1 * 0.5^9

P(x = 1) = 10 * 0.5 * 0.001953125

P(x = 0) = 0.009765625

P(x ≤ 1) = 0.0009765625 + 0.009765625

P(x ≤ 1) = 0.0107421875