Let p be the probability that a positive score is obtained on this exam when a student randomly selects for ea

Question

Let p be the probability that a positive score is obtained on this exam when a student randomly selects for each of the 20 questions from the choices A, B, C, D, E. Which of the following is closest to p ?

Answer 1

What follows?

Answer 2

p = (20 choose 14) * (1/5)^14 * (4/5)^6 + (20 choose 15) * (1/5)^15 * (4/5)^5 + ... + (20 choose 20) (1/5)^20

that is assuming a passing grade is 70% (14/20). this is simply a binomial distribution with chance of getting the correct answer 1 out of 5.

Answer 3

4 correct answers would be the most probable..

if you want the probability of getting each of the possible 21 (0-20) scores, they are

let i = score obtained
pmf = (20! / (i! *(20-i)!)) 1/5^i * 4/5^(20-i)