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Basic Stats/Prob Question.

  • 16-10-2009 6:12pm
    #1
    allinorfold
    Closed Accounts Posts: 10 ✭


    Four towns A, B, C, and D in a remote mountainous region are connected by roads directly
    linking AB, AC, BD, and CD.

    On any given day each of these fours road is open (available for travel) with probability p, independently of all the others. (Otherwise it is closed by an avalanche.)
    (a) Find the probability that, on a given day, it is possible to travel from A to D along
    the route ABD.
    (b) Find the probability that, again on a given day, it is possible to travel somehow from
    A to D.

    Suppose now that the road AC is permanently closed, but that a new road is built
    directly connecting B and C.
    This new road is open (available for travel) with probability 1. Find the new proba-
    bility that, again on a given day, it is possible to travel from A to D.


Comments

  • #2
    allinorfold
    Closed Accounts Posts: 10 ✭allinorfold


    I have the answers and (a) and (b) are extremely straightforward I know.
    For part (c) I also thought it was extremely simple but the lecturer's suggested solution is extremely complex. So much so, that I'm not sure if it was necessary. I'd like to see some other peoples' thoughts on this?


  • #3
    RoundTower
    Registered Users, Registered Users 2 Posts: 5,083 ✭✭✭RoundTower


    it looks quite simple to me, though not as simple as the other two.

    so long as you realize that (Probability ABD is open) and (Probability ABCD is open) are not independent events, you should be able to solve it easily.


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