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Консультация № 178566
22.05.2010, 18:16
0.00 руб.
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2
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Доброе время суток уважаемые эксперты.
Задача по теории вероятностей.
Имеются 5 отрезков длиной 1, 3, 5, 7 и 9 см. Определить вероятность того, что из 3-х наудачу взятых отрезков (из этих пяти) можно построить треугольник.
Задача по теории вероятностей.
Имеются 5 отрезков длиной 1, 3, 5, 7 и 9 см. Определить вероятность того, что из 3-х наудачу взятых отрезков (из этих пяти) можно построить треугольник.
Обсуждение
23.05.2010, 09:47
общий
это ответ
Здравствуйте, LfiN.
Из пяти отрезков выбрать три можно N = C53 = 10 способами. Для того, чтобы из трех отрезков можно было составить треугольник, необходимо, чтобы длина каждого из отрезков была меньше суммы двух других. Этому условию удовлетворяют следующие тройки отрезков:
1) 3, 5, 7;
2) 3, 7, 9;
3) 5, 7, 9.
То есть существует три таких тройки (n = 3). Следовательно, искомая вероятность равна P = n/N = 3/10 = 0,3.
С уважением.
Из пяти отрезков выбрать три можно N = C53 = 10 способами. Для того, чтобы из трех отрезков можно было составить треугольник, необходимо, чтобы длина каждого из отрезков была меньше суммы двух других. Этому условию удовлетворяют следующие тройки отрезков:
1) 3, 5, 7;
2) 3, 7, 9;
3) 5, 7, 9.
То есть существует три таких тройки (n = 3). Следовательно, искомая вероятность равна P = n/N = 3/10 = 0,3.
С уважением.
5
Благодарю
Об авторе:
Facta loquuntur.
Facta loquuntur.
Неизвестный
23.05.2010, 20:28
общий
это ответ
Здравствуйте, LfiN.
Треугольник можно построить только из следующих отрезков (сумма любых двух сторон треугольника должна быть больше третьей): 3,5,7; 5,7,9; 3,7,9- всего 3 комбинации отрезков.
Общее кол-во исходов выбрать три отрезка из 5: Сочетания из 5 по 3.
С(5,3) = 10.
Вероятность построить треугольник – это отношение кол-ва благоприятных исходов к общему кол-ву исходов = 3/10 = 0,3
Треугольник можно построить только из следующих отрезков (сумма любых двух сторон треугольника должна быть больше третьей): 3,5,7; 5,7,9; 3,7,9- всего 3 комбинации отрезков.
Общее кол-во исходов выбрать три отрезка из 5: Сочетания из 5 по 3.
С(5,3) = 10.
Вероятность построить треугольник – это отношение кол-ва благоприятных исходов к общему кол-ву исходов = 3/10 = 0,3
5
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