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Math Help - Dependent Events

  1. #1
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    Dependent Events

    Morgan believes she has a 60% chance that she will be late for class if she misses the 8:00 bus. There is a 80% chance that she will miss the 8:00 bus on any day.

    A) What is the probability that she will miss her bus tomorrow, but still be on time?

    B) If there is a 90% chance that Morgan will be late, even if she catches the 8:00 bus, what is the probability that she will be late on any given day.


    I know the formula I need to use, I just don't know which percentages go in which part of the formula? Would for part A this be correct??

    p(A) =
    p(B) = 80%
    p(AandB)= 60%

    p(AandB) = p(A) x p(B)
    p(A) = 0.60/0.80
    p(A) = 0.48 = 48%
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  2. #2
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    Re: Dependent Events

    Quote Originally Posted by momofmaxncoop View Post
    Morgan believes she has a 60% chance that she will be late for class if she misses the 8:00 bus. There is a 80% chance that she will miss the 8:00 bus on any day.
    A) What is the probability that she will miss her bus tomorrow, but still be on time?
    B) If there is a 90% chance that Morgan will be late, even if she catches the 8:00 bus, what is the probability that she will be late on any given day.
    Let L be the event of being late to class.
    Let M be the event of missing the bus.
    The statement “a 60% chance that she will be late for class if she misses the 8:00 bus” seems to me to mean “given that the bus is missed, she will be late for class”. \mathcal{P}(L|M)=0.6
    That is the way that I read the “If…then…” form.

    So part a) asks \mathcal{P}(L\cap M)
    Last edited by Plato; August 25th 2011 at 12:55 PM.
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  3. #3
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    Re: Dependent Events

    Quote Originally Posted by momofmaxncoop View Post
    Morgan believes she has a 60% chance that she will be late for class if she misses the 8:00 bus. There is a 80% chance that she will miss the 8:00 bus on any day.

    A) What is the probability that she will miss her bus tomorrow, but still be on time?

    B) If there is a 90% chance that Morgan will be late, even if she catches the 8:00 bus, what is the probability that she will be late on any given day.


    I know the formula I need to use, I just don't know which percentages go in which part of the formula? Would for part A this be correct??

    p(A) =
    p(B) = 80%
    p(AandB)= 60%
    No, you were told that P(A)= 80% and P(A|B) (probability A happens given that B happens) is 60%. P(A and B) = P(A|B)*P(B). However, "A" here is "she will be late for class". You want P(A* and B) where A* is the complement of A, the probability that she is NOT late for class. If P(A|B)= 80% what is P(A*|B)?

    p(AandB) = p(A) x p(B)
    p(A) = 0.60/0.80
    p(A) = 0.48 = 48%
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  4. #4
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    Re: Dependent Events

    Quote Originally Posted by HallsofIvy View Post
    No, you were told that P(A)= 80% and P(A|B) (probability A happens given that B happens) is 60%. P(A and B) = P(A|B)*P(B). However, "A" here is "she will be late for class". You want P(A* and B) where A* is the complement of A, the probability that she is NOT late for class. If P(A|B)= 80% what is P(A*|B)?
    Halls you seem to be agreeing with my reading of this. But why?
    Mind you I think we are both right.
    I just cannot find a definitive justification of it
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    Re: Dependent Events

    @Plato... I too agree with your statement The statement “a 60% chance that she will be late for class if she misses the 8:00 bus” seems to me to mean “given that the bus is missed, she will be late for class”. But, won't the A part of the question ask for the p(A*|B) , that is the probability of the student being on time despite missing the bus, ?
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  6. #6
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    Re: Dependent Events

    Quote Originally Posted by MAX09 View Post
    The statement “a 60% chance that she will be late for class if she misses the 8:00 bus” seems to me to mean “given that the bus is missed, she will be late for class”. But, won't the A part of the question ask for the p(A*|B) , that is the probability of the student being on time despite missing the bus, ?
    That is correct. Part a) wants the value of P(L^*\cap M)
    But that is P(L^*|M)P(M).

    From part b) we are given P(L|M^*)=0.9.
    Then asked to find P(L).

    Note that in general P(H^*|K)=1-P(H|K).
    BUT P(H|K^*)\ne 1-P(H|K).
    Last edited by Plato; August 25th 2011 at 12:29 PM.
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  7. #7
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    Re: Dependent Events

    Quote Originally Posted by Plato View Post
    I am posting this because I simply do not know how one reads the English here.
    Let L be the event of being late to class.
    Let M be the event of missing the bus.
    The statement “a 60% chance that she will be late for class if she misses the 8:00 bus” seems to me to mean “given that the bus is missed, she will be late for class”. \mathcal{P}(L|M)=0.6
    That is the way that I read the “If…then…” form.

    One the other hand, it seems reasonable to argue that the phrase means and, as in \mathcal{P}(L\cap M)=0.6

    Does anyone have a point view on this difference?
    If so, can you support that point of view?
    I was reading it exactly like you were, that is why I was asking for help and feedback on how about going on to answer the question.
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  8. #8
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    Re: Dependent Events

    Quote Originally Posted by momofmaxncoop View Post
    I was reading it exactly like you were, that is why I was asking for help and feedback on how about going on to answer the question.
    See reply #6.
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