chung 發問於 科學及數學數學 · 5 年前

probability We randomly choose three vertices from an octagonal pyramid.?

We randomly choose three vertices from an octagonal pyramid.If the probability that at least two chosen vertices lie on the same edge is a/b in lowest form, find the value of a+b.

更新:

the answer is 38,i dont understand

1 個解答

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  • 5 年前
    最愛解答

    P(at least two chosen vertices lie on the same edge )

    = 1 - P(3 chosen vertices have no any 2 lie on the same edge)

    = 1 - P(3 chosen vertices at the base) * P(Such 3 vertices at the base have no any 2 lie on the same edge)

    = 1 - P(3 chosen vertices at the base) * P(a such vertices at the base is not near other 2's) * (1 - P(other 2's

    lie on the same edge))

    = 1 - C(8,3)/C(9,3) * C(5,2)/C(7,2) * (1 - 4/C(5,2))

    = 1 - 56/84 * 10/21 * (1 - 4/10)

    = 1 - 2/3 * 2/7

    = 17/21 = a/b

    The value of a + b = 17 + 21 = 38.

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