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Probability 2

  1. Feb 18, 2006 #1
    Well I wish Arildno but I have this last one to crack...

    A town has three bus routes A, B and C. Route A has twice as many buses as each of B and C. Over a perido of time it has been found that, along a certain stretch of road, where the three routes converge, the buses on these routes run more than five minutes late 1/2, 1/5 and 1/10 of the time respectively.

    1) A bus is going down this stretch of road. What is the probability it is more than 5 minutes late?

    2) Comment on the size of the answer to 1) with the respect to the given probabilities 1/2, 1/5 and 1/10.

    3) An inspector, standing on this particular stretch of road, sees a bus that is more than five minutes late. Find the probability that it is a route B bus.

    Any help as I am very new to probabilities... thanks :smile:
     
  2. jcsd
  3. Feb 18, 2006 #2

    arildno

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    Irrespective of the lateness of a bus observed on the common stretch, what is the probability that it came from A? From B? From C?
     
  4. Feb 18, 2006 #3
    So for 1) we have

    p(more than 5 mins late) = 2/3 + 1/3 + 1/3 = 4/3
     
  5. Feb 18, 2006 #4

    arildno

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    Not at all.
    Try to answer my question first.
     
  6. Feb 18, 2006 #5
    from A is 2/3

    from B is 1/3

    from C is 1/3
     
  7. Feb 18, 2006 #6

    arildno

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    Do those add up to one?
     
  8. Feb 18, 2006 #7
    would it be 1/3, 1/3 and 1/3 then?
     
  9. Feb 18, 2006 #8

    arildno

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    No.
    You know that there are twice as many buses on the A route as on either of the other two.
     
  10. Feb 18, 2006 #9
    2/3, 1/6 and 1/6
     
  11. Feb 18, 2006 #10

    arildno

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    What is 2+1+1?
     
  12. Feb 18, 2006 #11

    0rthodontist

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    Well, they added up to 1 that time but you do not have the right answer Natasha. Try making the situation more concrete. What if routes B and C have only one bus each? Then what would the probability be that a given bus comes from A, B, or C?
     
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