Suppose you're at a college campus. 3/4 of the people on the campus are students or professors from that college, and the rest 1/4 aren't. When asked a question, students and professors from that college will give you a correct answer every time, and those that aren't from the college will give you a correct answer 3/8th of the time.
a) You stop a random person and ask for directions to place A belonging on campus and he gives you an answer. What is the probability that the answer is true?
b) You ask the same person the same question again and he gives you the exact same answer. What is the probability that answer is correct now?
Total probability theorem: P(A) = P(A|H1)P(H1) + P(A|H2)P(H2) + ... + P(A|Hn)P(Hn)
The Attempt at a Solution
Using the total probability theorem, I make two hypotheses:
H1:The person is from the college
H2:The person is not from the college
And the event:
A:The answer is correct
P(H1) = 3/4, P(H2) = 1/4, P(A|H1) = 1, P(A|H2) = 3/8
The probability for A would be:
P(A) = P(H1)P(A|H1) + P(H2)P(A|H2) = 3/4 + 1/4 * 3/8 = 0.84375
However, when it comes to part b), I am stuck. How do I proceed?