Question

Kenyin is taking a short multiple choice quiz with four questions on it. If each question has four choices and Kenyin guess at all the questions, what is the probability he gets exactly two of the three correct?

Answer 1

Kindly note that the question says 4; maybe the final question was intended to be the probability that he gets exactly 2 of the 4 correct. However. If it is the other way round. This a e procedure used in the solution should also be followed.

Answer:

0.21

Explanation:

Number of options = 4

One correct answer per option ; hence, the probability of success, p = 1/4 = 0.25

Using the binomial probability relation :

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

x = 2 ; n = 4

p = 0.25 ; 1 - p = 0.75

P(x = 2) = 4C2 * 0.25^2 * 0.75^2

P(x = 2) = 6 * 0.0625 * 0.5625

P(x = 2) = 0.2109375

P(x = 2) = 0.21 (2 decimal places)

Note : if the question was 3, then put, n = 3 instead of 4