A very short quiz has one multiplechoice question with N pos

A very short quiz has one multiple-choice question with N possible choices and one true or false question. Assume you are taking the quiz but do not have any idea what the correct answer is to either question, but you mark an answer anyway.

a. What is the probability that you have given the correct answer to both questions?
b. What is the probability that only one of the two answers is correct?
c. What is the probability that neither answer is correct?
d. What is the probability that only your answer to the multiple-choice question is correct?
e. What is the probability that you have only answered the true or false question correctly?

Solution

a) 1/n x 1/2 = 1/2n

b)if we get the multiple choice question right and the t/f question wrong,then the prob will be 1/nx 1/2=1/2n.
if we get the multiple choice question wrong and the t/f questoin rite then the prob is (n-1)/n x 1/2=(n-1)/2n

total probaibily = 1/2n + (n-1)/2n = 1/2

c)(n-1)/n x 1/2 = (n-1)/2n

d)1/n

e)1/2

c)