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probabilityWe randomly choose three vertices from an octagonal pyramid.?
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最佳解答:
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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probabilityWe randomly choose three vertices from an octagonal pyramid.?
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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最佳解答:
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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