Question

A test contains 6 multiple-choice questions . Each question has one correct answer to choose from 3 options. If you answer all 6 questions by guessing randomly , find the probability of getting at least one question wrong.

Answer 1

A test contains 6 multiple choice questions.

let p = probability of correct question = 1/3

and q = 1- p = 2/3

P(at least one question wrong)

= 1 - P(All questions are correct)

= 1 - ((6 C 6) * (1/3)^6 * (2/3)^0)

=1 - 0.00002143347

= 0.9999785

Note: Here I used /.....

The binomial distribution formula is:

b(x; n, P) = nCx * Px * (1 – P)n – x

Where:
b = binomial probability
x = total number of “successes” (pass or fail, heads or tails etc.)
P = probability of a success on an individual trial
n = number of trials