Anonymous asked in 科學及數學數學 · 1 decade ago

math and state question no.9

The 10 volumes of the a series of books are arranged at random on a bookshelf. What is the probability that the books are arranged (a)in order of the volume number? b)with the 1st volume on the left end and the 10th volume on the right end? c)with the 2nd and 3rd volumes together?

1 Answer

  • 1 decade ago
    Favorite Answer

    a. P(in order)

    = 1 / 10P10(Since there is only one possibleoutcome)

    = 2.756 X 10-7

    b. P.S. We don’t haveto consider the rest of the 8 books.

    P(1stvolume on the left hand and the 10th volume on the right end)

    = 1 / 10P2

    = 0.01111

    c. Consider the cases:

    When 2nd ison the left, 3rd must be on the right of 2nd (1 case)

    When 2nd isin the middle of the 8 spaces, 3rd must be next to 2nd (8X 2 = 16 cases)

    When 2nd ison the right, 3rd must be on the left of 2nd (1 case)

    P(2nd and 3rdtogether)

    = (1 + 16 + 1) / 10P2

    = 0.2

    Source(s): Myself~~~
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