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Консультация № 137821
21.05.2008, 22:53
0.00 руб.
0
1
1
Из 10 одинаковых коробок шаров, 6 содержит красные шары, 4 - белые шары. Случайно выбирают 4 коробки.
Какова вероятность ,что
1)в двух коробках шары белого цвета,а в других красногоцвета
2)все 4 упаковки содержат шары одного цвета.
Какова вероятность ,что
1)в двух коробках шары белого цвета,а в других красногоцвета
2)все 4 упаковки содержат шары одного цвета.
Обсуждение
Неизвестный
22.05.2008, 00:14
общий
это ответ
Здравствуйте, Бобриков Василий Иванович!
1) Всего есть C<sub>6</sub><sup>2</sup>=6!/(2!*4!)=15 способов выбрать 2 красных шара из 6.
А выбрать 2 шара из 4-ех белых=C<sub>4</sub><sup>2</sup>=4!/(2!*2!)=6.
Всего существует C<sub>10</sub><sup>4</sup>=10!/(4!*6!)=210 способов выбрать 4 шара из 10.
Искомая вероятность=C<sub>6</sub><sup>2</sup>*C<sub>4</sub><sup>2</sup>/C<sub>10</sub><sup>4</sup>=15*6/210=3/7
2) Таков вариант возможен если все коробки с шарами красного цвета (вероятность этого события равна C<sub>6</sub><sup>4</sup>/C<sub>10</sub><sup>4</sup>) или же все коробки белого цвета (вероятность этого события равна C<sub>4</sub><sup>4</sup>/C<sub>10</sub><sup>4</sup>).
Общая вероятность этих событий равна: (C<sub>6</sub><sup>4</sup>+C<sub>4</sub><sup>4</sup>)/(C<sub>10</sub><sup>4</sup>)=(6!/(4!*2!)+4!/(4!*0!))/(10!/(4!*6!))=16/210=8/105
Удачи!
1) Всего есть C<sub>6</sub><sup>2</sup>=6!/(2!*4!)=15 способов выбрать 2 красных шара из 6.
А выбрать 2 шара из 4-ех белых=C<sub>4</sub><sup>2</sup>=4!/(2!*2!)=6.
Всего существует C<sub>10</sub><sup>4</sup>=10!/(4!*6!)=210 способов выбрать 4 шара из 10.
Искомая вероятность=C<sub>6</sub><sup>2</sup>*C<sub>4</sub><sup>2</sup>/C<sub>10</sub><sup>4</sup>=15*6/210=3/7
2) Таков вариант возможен если все коробки с шарами красного цвета (вероятность этого события равна C<sub>6</sub><sup>4</sup>/C<sub>10</sub><sup>4</sup>) или же все коробки белого цвета (вероятность этого события равна C<sub>4</sub><sup>4</sup>/C<sub>10</sub><sup>4</sup>).
Общая вероятность этих событий равна: (C<sub>6</sub><sup>4</sup>+C<sub>4</sub><sup>4</sup>)/(C<sub>10</sub><sup>4</sup>)=(6!/(4!*2!)+4!/(4!*0!))/(10!/(4!*6!))=16/210=8/105
Удачи!
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