(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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 [tex]\frac{3}{4}[/tex] (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.

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?

2. Relevant equations

[tex]P(A|B)=\frac{P(B|A)P(A)}{P(B)}[/tex] {Baye's Theorem}

[tex]P(A\cap B) = P(A)P(B)[/tex] {For independent events A and B}

[tex]P(A\cup B) = P(A)+P(B)-P(A\cap B)[/tex]

3. The attempt at a solution

My approach was to use Baye's Theorem. The problem is that I dont have any prior probabilities.

Let P(P) be the probability that the person is a prof.

P(S) '' '' is a student.

P(E) '' '' answer is East.

P(T) " " correct answer is given.

Now

[tex]P(T|E) = \frac{P(E|T)P(T)}{P(E)}[/tex]

with

[tex]P(T)=P(S \cap T \cup P \cap T)[/tex]

and [tex]P(E) = 0.5[/tex].

Is this the right way to go about it?

As a heuristic, a later question says that if you ask the same person again, and they answer East, you need to show that the probability that East is True is 1/2.

Any points in the right direction would be most welcome

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# Homework Help: Lost at MIT probability

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