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Math Help - Person A and B enter a cafe b/w 8 am and 9am..

  1. #1
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    Person A and B enter a cafe b/w 8 am and 9am..

    Hi guys .
    So I've been working on this problem for a while now I thought I had it but My lecturer said Nope. And there was a simpler way involving a graph. ANY help would make you so utterly loved and grant you supernatural powers.
    QUESTION: wo people A and B will be arriving at a small coffee bar at any time between 8am
    and 9am equally likely. Each of them will stay exactly 10 minutes in the bar. What
    is the probability that they will meet each other in the bar? (Hint: Let (X, Y ) be the
    arrival times (in minutes) of A and B, and let M be the event that they will meet each
    other. Then plot the sample space S and the event M, from which try to find the
    probability of M.)
    My attempt: Person A will meet person B if B arrives less than 10 minutes before A or less than 10 minutes after A.
    Case 1:
    If person A arrives after 8:10 AND before 8:50. The probability that person A meets person B P(A meets B) is given by.
    P(AmeetsB)=20/60=1/3

    Case2:
    If Person A arrives say 'm' minutes after 8am or m minutes before 9am., time interval is 0<=m<=10

    P(A meets B)=(10+m)/60
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  2. #2
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    Re: Person A and B enter a cafe b/w 8 am and 9am..

    Quote Originally Posted by waytoocool View Post
    Hi guys .
    So I've been working on this problem for a while now I thought I had it but My lecturer said Nope. And there was a simpler way involving a graph. ANY help would make you so utterly loved and grant you supernatural powers.
    QUESTION: wo people A and B will be arriving at a small coffee bar at any time between 8am
    and 9am equally likely. Each of them will stay exactly 10 minutes in the bar. What
    is the probability that they will meet each other in the bar? (Hint: Let (X, Y ) be the
    arrival times (in minutes) of A and B, and let M be the event that they will meet each
    other. Then plot the sample space S and the event M, from which try to find the
    probability of M.)
    Plot a 60 \times 60 grid,
    Plot in that region this set, \left\{ {(x,y):\left| {x - y} \right| \le 10} \right\}.
    The probability will be the ratio of the areas.
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  3. #3
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    Re: Person A and B enter a cafe b/w 8 am and 9am..

    Oh I see now. Thank you Plato!.
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