Question

Imagine that Exam 1 for Statistics 2160 this term will have 53 questions. Each question has 5 multiple choice options, giving you a probability of 0.2 of getting each question right purely by guessing. Assuming that you guess on all questions, what is the probability that you get no more than 9 questions right on your exam?

Question 12 options:

1)

0.0618

2)

0.3643

3)

0.2408

4)

0.6357

5)

0.1235

Answer 1

ANSWER:

Given that,

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

P( X < 9) = P(X=8) + P(X=7) + P(X=6) + P(X=5) + P(X=4) + P(X=3) + P(X=2) + P(X=1) +...+P(X=0)
= ( 53 9 ) * 0.2^9 * ( 1- 0.2 ) ^44 + ( 53 8 ) * 0.2^8 * ( 1- 0.2 ) ^45 + ( 53 7 ) * 0.2^7 * ( 1- 0.2 ) ^46 + ( 53 6 ) * 0.2^6 * ( 1- 0.2 ) ^47 + ( 53 5 ) * 0.2^5 * ( 1- 0.2 ) ^48 + ( 53 4 ) * 0.2^4 * ( 1- 0.2 ) ^49 + ( 53 3 ) * 0.2^3 * ( 1- 0.2 ) ^50 + ( 53 2 ) * 0.2^2 * ( 1- 0.2 ) ^51 + ( 53 1 ) * 0.2^1 * ( 1- 0.2 ) ^52 + .... +( 53 0 ) * 0.2^0 * ( 1- 0.2 ) ^53
= 0.3643

2nd option is correct.