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Math Help - Book Reading

  1. #1
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    Book Reading

    You read 8 plays over 2 days, 4 plays per day.

    If Hamlet and Macbeth are two plays, what is the probability that you read them on the same day?
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  2. #2
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    Hello, thefirsthokage!

    Here's one approach . . .


    You read 8 plays over 2 days, 4 plays per day.

    If Hamlet and Macbeth are two of the plays,
    what is the probability that you read them on the same day?

    There are: \binom{8}{4,4} = 70 ways to read the books.


    There are two cases to consider:

    If you read Hamlet and Macbeth on the first day,
    . . there are \binom{6}{2} = 15 choices for the other 2 books read the first day.
    . . The other 4 books are read the second day.

    If you read Hamlet and Macbeth on the second day,
    . . there are \binom{6}{2} = 15 choices for the other 2 books read the second day.
    . . The other 4 books are read the first day.

    Hence, there are 15 + 15 \:=\:30 ways that Hamlet and Macbeth can be read on the same day.


    Therefore: P(\text{Hamlet \& Macbeth, same day}) \:=\:\frac{30}{70} \:=\:\frac{3}{7}

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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by thefirsthokage View Post
    You read 8 plays over 2 days, 4 plays per day.

    If Hamlet and Macbeth are two plays, what is the probability that you read them on the same day?
    Prob H read on day1 is 4/8, prob M read on day 1 given that H read on day 1
    is 3/7. Therefore prob both read on day 1 is (4/8)(3/7)~=0.214.

    (that is there are 4 slots out of 8 which are on day 1 to read H, but once
    H is allocated to a slot on day 1 there remain 7 slots of which 3 are on
    day 1 available for M.)

    The prob that they are both read on dy 2 is the same, so the prob that they
    are read on the same day is ~=2x0.214=0.428

    RonL
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