Stats Question (Please Help)

Question

A quiz has 10 multiple choice questions each with 4 answers that are equally likely to be the correct one. Suppose that the quiz takers need to score 7 corrects out of 10 to pass. Answer the following questions when the quiz taker selects the answers randomly

a) Probability of marking exactly 3 incorrect answers.

b) Probability of passing.

Answer 1

x = number of correct answers following binomial distribution

P(x = k) = n! p^k * (1-p)^(n-k) Here n = 10, p = 0.25 (one out of every 4 answers),

----

k! (n-k)!

a) probability of getting exactly 3 wrong is the same probability of getting exactly 7 correct. Use above equation with k = 7

P(x = 7) = 10!

----- (0.25)^7 (0.75)^3

7! 3!

b) probability of passing equals probability of getting either 7, 8, 9 or 10 correct. Compute P(x=7) + P(x=8) + P(x=9) + P(x=10)