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Math Help - probability Mr. Smith will miss work

  1. #1
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    Question probability Mr. Smith will miss work

    Hi!
    Can you hep me with this?

    Mr. Smith can drive to work along the shortest path or bypass.
    He drives the shortest path in 36% cases. The probabilty he will get stuck in traffic jam
    on the shortest road is 20%, in addition in the case of traffic jam he can miss the work with the probability of 10%.
    The probability to get stuck in traffic on bypass road is 8%, in addition after getting out of traffic jam, he can
    miss work with the probability of 24%.


    a) what is the probability, Mr. Smith will miss the work?
    b) If Mr. Smith misses work, what is the probability, he was driving bypass road?

    Do I have to use full probability, Bayse formula or something else?
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  2. #2
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    Re: probability Mr. Smith will miss work

    Quote Originally Posted by Kiiefers View Post
    Hi!
    Can you hep me with this?

    Mr. Smith can drive to work along the shortest path or bypass.
    He drives the shortest path in 36% cases. The probabilty he will get stuck in traffic jam
    on the shortest road is 20%, in addition in the case of traffic jam he can miss the work with the probability of 10%.
    The probability to get stuck in traffic on bypass road is 8%, in addition after getting out of traffic jam, he can
    miss work with the probability of 24%.


    a) what is the probability, Mr. Smith will miss the work?
    b) If Mr. Smith misses work, what is the probability, he was driving bypass road?

    Do I have to use full probability, Bayse formula or something else?
    Law of total probability is sufficient. You would like P(\overline{W}) where W is the event that Mr.Smith shows to work. Let S be the event that Mr.Smith takes the shortest path.

    P(\overline{W}) = P(\overline{W} | S) P(S) + P(\overline{W} | \overline{S}) P(\overline{S})

    Now, P(\overline{W} | S) = 0.2(0.1) and P(\overline{W} | \overline{S}) = 0.08(0.24), and I'll let you take it from here.
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  3. #3
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    Re: probability Mr. Smith will miss work

    thanks
    Last edited by Kiiefers; April 13th 2013 at 03:49 AM.
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  4. #4
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    Re: probability Mr. Smith will miss work

    Quote Originally Posted by majamin View Post
    Law of total probability is sufficient. You would like P(\overline{W}) where W is the event that Mr.Smith shows to work. Let S be the event that Mr.Smith takes the shortest path.

    P(\overline{W}) = P(\overline{W} | S) P(S) + P(\overline{W} | \overline{S}) P(\overline{S})

    Now, P(\overline{W} | S) = 0.2(0.1) and P(\overline{W} | \overline{S}) = 0.08(0.24), and I'll let you take it from here.
    So it will be like this?

    P=0,36*0,2*0,1+0,64*0,08*0,24
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  5. #5
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    Re: probability Mr. Smith will miss work

    Yes. That looks correct.
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