very difficult problem from MIT

VijaKhara@gmail.com · science forum beginner Joined: 30 Sep 2005 Posts: 26

Hi I see this problem from MiT's website.

"You are lost in the campus of MIT, where the population is entirely
composed of brilliant students and absent-minded professors. The
students comprise two-thirds of the population, and any one student
gives a correct answer to a request for directions with probability 3/4
.. (Assume answers to repeated questions are independent, even if the
question and the person asked are the same.) If you ask a professor for
directions, the answer is always false.
(a) You ask a passer-by whether the exit from campus is East or West.
The answer is East. What is the probability this is correct?
(b) You ask the same person again, and receive the same reply. Show
that the probability that this second reply is correct is 1/2 .
(c) You ask the same person again, and receive the same reply. What is
the probability that this third reply is correct?
(d) You ask for the fourth time, and receive the answer East again.
Show that the probability it is correct is 27/40 .
(e) Show that, had the fourth answer been West instead, the probability
that East is nevertheless correct is 9/10 .

Your friend, Ima Nerd, happens to be in the same position as you are,
only she has reason to believe a-priori that, with probability p , East
is the correct answer.
(f) Show that whatever answer is first received, Ima continues to
believe that East is correct with probability p .
(g) Show that if the first two replies are the same (that is, either WW
or EE), Ima continues to believe that East is correct with probability
p.

++++++++++++

The outcome of this problem is too complicated:
Sample space:
S1: Prof, Student
S2: West, East
S3: True, False

for the question a:

I can find the
P(correct)=P(Correct|Prof)P(Prof)+P(Correct|Student)P(student)=1/2

Now we should find P(Correct|West) Confused

??

I am running into a blocked road here. I think I don't have enough
information to go on.

Plz help

Thanks

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