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Math Help - conditional probability question

  1. #1
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    conditional probability question

    Hi;
    Jean always goes to work by bus or taxi,If one day she goes to work by bus the probability
    that she goes by taxi the next day is 0.4,If one day she goes by taxi the probability she goes by bus the next day is 0.7

    Given that on monday she goes by bus,Whats the probabilty she goes by taxi on wednesday.

    What I have
    On monday she has an equal chance of taxi or bus probabilty=0.5each
    On tuesday she has a 0.4 probability by taxi and 0.6 by bus but we don,t know which she took.

    If she took the bus she has a 0.4 probability by taxi and 0.6 probability by bus
    If she took a taxi she has a 0.7 probability by bus and a 0.3 probabity by taxi.



    Stuck here
    Do I add the probabilities of the wednesday ie 0.4(taxi) + 0.3(taxi) and just divide them by 2?
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  2. #2
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    Re: conditional probability question

    You are given that she took the bus on Monday ("Given that on monday she goes by bus..."). So your statement "On monday she has an equal chance of taxi or bus probabilty=0.5each" is wrong. With 100% probability, she took the bus on Monday.
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  3. #3
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    Re: conditional probability question

    Of course I missed that bit
    Heres A badly drawn tree diagram of what I think is correct


    conditional probability question-untitled.jpg
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  4. #4
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    Re: conditional probability question

    Here's a hint - look at the formula for Total Probability: P[A] = P[A|B]*P[B] + P[A|C]*P[C], (given events A,B,C)
    You could write: P[Wed=Taxi] = P[Wed=Taxi | Tue=Taxi]*P[Tue=Taxi] + P[Wed=Taxi | Tue=Bus]*P[Tue=Bus]

    Now you need to figure out how to get P[Tue=Taxi] and P[Tue=Bus]. Again, P[Mon=Bus] = 100%, and P[Mon=Taxi] = 0%.
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  5. #5
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    Re: conditional probability question

    Oops- I just saw your drawing.. taking a look.
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  6. #6
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    Re: conditional probability question

    OK, I modified the drawing a little. Does this make sense? conditional probability question-prob.jpg
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  7. #7
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    Re: conditional probability question

    Yes thanks.
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