Problema Solution
On a multiple choice quiz each question has 4 possible answers of which 1 is correct. Find the probability of getting exactly 6 correct out of 8 questions if you answer them purely by guessing.
Answer provided by our tutors
n = 8 questions
r = 6 questions exactly correct
n – r = 8 - 6 = 2
p = 1/4 = 0.25 = probability of guessing the correct answer on a question.
q = 1 - p = 1 - 0.25 = 0.75 = probability of not guessing the correct answer on a question
we will use the formula for binomial probability
nCr * p^r * q^(n-r)
P(guessing 6 correct) = 8C6 x (0.25)^6 x (0.75)^2 = 28 x (0.25)^6 x (0.75)^2 = 0.00384521
where 8C6 = 8!/((8 - 6)!6!) = 28
The probability of getting exactly six questions correct is 0.38%.