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Консультация № 197969
13.03.2020, 09:41
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Здравствуйте! Прошу помощи в следующем вопросе:
В урне 5 белых, 6 черных и 9 красных шаров. Из урны наугад извлекаются 3 шара.
Какова вероятность того, что:
1) все они – разных цветов?
2) два из них одного цвета, а третий – другого?
В урне 5 белых, 6 черных и 9 красных шаров. Из урны наугад извлекаются 3 шара.
Какова вероятность того, что:
1) все они – разных цветов?
2) два из них одного цвета, а третий – другого?
Обсуждение
26.07.2022, 07:21
общий
это ответ
Здравствуйте, olegpetrov111998!
Число способов выбрать наугад три шара из двадцати равно
а) Выбрать один шар белого цвета из пяти можно пятью способами, один чёрный шар из шести -- шестью способами, один красный шар из девяти -- девятью способами. Значит, искомая вероятность равна
б) Поставленному условию (два шара одного цвета, а третий -- другого) соответствуют следующие случаи:
- два белых шара и один чёрный. Число способов составляет
- два чёрных шара и один белый. Число способов составляет
- два белых шара и один красный. Число способов составляет
- два красных шара и один белый. Число способов составляет
- два чёрных шара и один красный. Число способов составляет
- два красных шара и один чёрный. Число способов составляет
Значит, искомая вероятность равна
Для косвенной проверки полученных результатов вычислим число способов вынуть три шара одного цвета:
Тогда число всех способов равно 
как и должно быть.
Число способов выбрать наугад три шара из двадцати равно
а) Выбрать один шар белого цвета из пяти можно пятью способами, один чёрный шар из шести -- шестью способами, один красный шар из девяти -- девятью способами. Значит, искомая вероятность равна
б) Поставленному условию (два шара одного цвета, а третий -- другого) соответствуют следующие случаи:
- два белых шара и один чёрный. Число способов составляет
- два чёрных шара и один белый. Число способов составляет
- два белых шара и один красный. Число способов составляет
- два красных шара и один белый. Число способов составляет
- два чёрных шара и один красный. Число способов составляет
- два красных шара и один чёрный. Число способов составляет
Значит, искомая вероятность равна
Для косвенной проверки полученных результатов вычислим число способов вынуть три шара одного цвета:
Тогда число всех способов равно как и должно быть.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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