1. Not finding help here? Sign up for a free 30min 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!

Probability Question

  1. Sep 9, 2004 #1
    It is known that the inhabitants of an island tell the truth 1/3 of the time and lie 2/3 of the time. On an occasion, one person made a statement and the person after him said the statement was true. What is the probability that the statement is actually true?
     
  2. jcsd
  3. Sep 9, 2004 #2
    I would think 1/9 but i dont actually remember how to do probablility. :wink:
     
  4. Sep 10, 2004 #3

    Claude Bile

    User Avatar
    Science Advisor

    Consider the 4 possibilities -
    1st person truthful, 2nd person truthful
    1st person truthful, 2nd person lying
    1st person lying, second person truthful
    1st person lying, second person lying.

    Work out how probable each possibility is, then work out which possibilities actually result in the second person claiming the first person is truthful. The rest should be easy.

    Claude.
     
  5. Sep 10, 2004 #4
    Here's what I did:

    P (1st telling truth | second says first is telling truth) =
    P (1st telling truth and second says first is telling truth) / [P(1st is telling truth and second says first is telling truth) + P(1st is lying and second says first is selling truth)]
    = 1/3
     
    Last edited by a moderator: Sep 10, 2004
  6. Sep 10, 2004 #5
    Or they are telling true , or they are lying .

    The answer is ( 1/3 * 1/3 ) / ( 1/3 * 1/3 + 2/3 * 2/3 ) = 1/5 .
     
  7. Sep 10, 2004 #6

    Fredrik

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    The answer is 1/3. A good way to see this is to do what Claude Bile suggested. Look at the four different "possibilities" one at a time. But you should also ask yourself if they're all really possible. (Big hint: They're not).
     
  8. Sep 10, 2004 #7
    I can not say something truthful, and then have my neighbor say something truthful also? theres a 1/3 chance that i would say something truthful, and a 1/3 chance that my neighbor would say something truthful.... no?
     
  9. Sep 11, 2004 #8

    Fredrik

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Suppose that you say "it's raining", and your neighbor says "what musky ox is saying is true".

    Which ones of the following alternatives are possible, and which ones aren't?

    1. You're telling the truth and he's telling the truth.
    2. You're telling the truth and he's lying.
    3. You're lying and he's telling the truth.
    4. You're lying and he's lying.

    Once you have figured that out, the rest will be very easy.
     
    Last edited: Sep 11, 2004
  10. Sep 11, 2004 #9
    The answer is not 1/3 . Let's follow the Claude's suggestion:


    The first pair of persons ocurrs with probability: 1/3 * 1/3 = 1/9
    The second pair ocurrs with probability: 1/3 * 2/3 = 2/9
    The third pair ocurrs with probability: 2/3 * 1/3 = 2/9
    The fourth pair ocurrs with probability: 2/3 * 2/3 = 4/9

    But, since the 2 persons agreed, we know only the first or the last case can be possible.
    So, the probability we have a truthful pair of persons is (1/9) / (1/9 + 4/9) = 1/5.

    This is classical Bayes. :smile:
     
    Last edited: Sep 11, 2004
  11. Sep 11, 2004 #10

    Fredrik

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Yes, you're right. I assigned probability 0 to the impossible "possibilities", but that's not the right way to do this. :redface:
     
  12. Sep 11, 2004 #11
    Well, in fact, you and Claude Bile did the job !

    I just followed yours suggestion... :smile:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Probability Question
  1. Probability question (Replies: 7)

  2. Probability question (Replies: 6)

  3. Probability Question (Replies: 4)

  4. Probability Question (Replies: 7)

  5. A probability question (Replies: 0)

Loading...