Question

Suppose that a multiple-choice test has 20 questiions, with choices a, b, c, and d. What is the probability of getting a 90% on the assumption that you are purely guessing? Please show all the steps.

Answer 1

Given: - multiple choice questions N = 20 four options A,B,C,D each of probability = 1/4 = 0.25 P = 0.25 q = 1-P = 0.75 N = 20 we have to find what is the probability of getting 90% by purely guessing For getting 90% we have to make 20 times 90/100 = 18 18 correct answers. Probability of getting 18 correct answers. P(x = 18) = nc_18 p^18 q^n-18 = 20C _18 (0.25)^18 q^20-18 = 20C_18 (0.25)^18 (0.75)^2 P(x = 18) = 1.55523 times 10^-9