1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Lost at MIT probability

  1. Oct 6, 2008 #1
    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.


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


    [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 :smile:
  2. jcsd
  3. Oct 6, 2008 #2
    Using a tree might make this easy to solve.

    P(student) * P(correct | student) = 2/3*3/4 = 6/12

    P(student) * P(~correct | student) = 2/3*1/4 = 2/12

    P(prof) * P(correct | prof) = 1/3*0 = 0

    P(prof) * P(~correct | prof) = 1/3*1 = 4/12

    Only one branch offers a correct answer since professors always answer incorrectly.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook