- #1

- 4

- 0

## Main Question or Discussion Point

A student is about to take a test, which consists of 12 multiple choice

questions. Each question has 4 possible answers, of which only one is

correct. The student will answer each question independently. For each

question, there is a probability 2/3 that he knows the correct answer;

otherwise, he picks an answer at random.

(a) Compute the probability that he will get exactly 9 questions right.

(b) compute the probability that his 12th answer will be his 9th correct answer

(c) Compute the probability that his 6th answer will be the 5th correct answer and his 12th answer will be the 9th correct answer.

Please help. For a, I think its binomial distribution, but I am having trouble with the probability, Is it simply 2/3 or must you factor in the probability for guessing. ie - probability is 2/3 +1/4 for the correct answer??

questions. Each question has 4 possible answers, of which only one is

correct. The student will answer each question independently. For each

question, there is a probability 2/3 that he knows the correct answer;

otherwise, he picks an answer at random.

(a) Compute the probability that he will get exactly 9 questions right.

(b) compute the probability that his 12th answer will be his 9th correct answer

(c) Compute the probability that his 6th answer will be the 5th correct answer and his 12th answer will be the 9th correct answer.

Please help. For a, I think its binomial distribution, but I am having trouble with the probability, Is it simply 2/3 or must you factor in the probability for guessing. ie - probability is 2/3 +1/4 for the correct answer??