10 multiple choice questions each with three possible answers only one of which is correct. A student guesses the answer to every question.

Question

(a)What is the probability that the student will answer the first six questions correctly and the rest incorrectly?
(b)What is the probability that the student will answer the 1st,2nd,4th,6th,7th,and 10th questions correctly and the rest incorrectly?
(c)How many ways can the student get exactly 6 correct answers?
(d)What is the probability that the student answers exactly 6 questions correctly?

Thank you so much for your help...

Answer 1

Prb(right) = 1/3, prb(wrong) = 2/3

a) you want
rrrrrrwwww
prb(rrrrrrwwww) = (1/3)^6(2/3)^4
= 16/59049

b) you want rrwrwrrwwr or the same as above

c) now the order does not matter, you want to choose 6 out of 10 which is
C(10,6) = 10!/(6!4!) = 210

d) prb(6 out of 10) = 210/59049 = 70/19683

Answer 2

You have a 5-question multiple-choice test. Each question has four choices. You don’t know any of the answers. What is the experimental probability that you will guess exactly three out of five questions correctly?

Answer 3

P(3 correct)= (.25)^3 x (.75)^2 combinations; 5C3= 5!/3!2!= 10
answer is 1/64 x 9/16 x 10 = 90/1024

Answer 4

I have no idea

Answer 5

fake