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Question abount independence events and conditional events

  1. Aug 28, 2005 #1
    Prove this questions using ration ideal in intuitive way.

    Prove this implications and explain the results:

    (a) A _|_ B => not A _|_ not B, onde _|_ means that events A and B are independent.

    (b)[ P(A|C) >= P(B|C) ] and [ P(A|not C) >= P(B|not C) ] ==> P(A) > P(B)
     
    Last edited: Aug 28, 2005
  2. jcsd
  3. Aug 28, 2005 #2
    Question about who tells the truth.

    Interesting question:

    " A says that B told him that C lied ".

    If each of these person tells the truth with probability p, what is the probability that C lied ?
     
  4. Aug 29, 2005 #3

    EnumaElish

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    [tex]A \perp B \longrightarrow P(A|B) = P(A) \longrightarrow \frac{P(A \& B)}{P(B)} = P(A) \longrightarrow[/tex]

    [tex]\frac{P(A) - P(A \& \~B)}{1 - P(\~B)} = P(A) \longrightarrow
    \frac{[1 - P(\~A)] - [P(\~B) - P(\~A \& \~B)]}{1 - P(\~B)} = 1 - P(\~A) \longrightarrow [/tex]

    [tex]1 - P(\~A) - P(\~B) + P(\~A \& \~B) = 1 - P(\~A) - P(\~B) + P(\~A)P(\~B) \longrightarrow \frac{P(\~A \& \~B)}{P(\~B)} = P(\~A) \longrightarrow \~A \perp \~B[/tex]
     
  5. Aug 30, 2005 #4
    {p^2+(1-p)^2}/{3p^2+(1-p)^2}
     
  6. Aug 31, 2005 #5
    The above is the answer to the question
    "Given " A says that B told him that C lied ".,what is the pr that c lied"
     
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