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Консультация № 200823
13.05.2021, 18:25
0.00 руб.
13.05.2021, 19:12
0
1
1
Здравствуйте! У меня возникли сложности с таким вопросом:
В урне находятся 2 красных, 3 синих и 2 зеленых шара. Из неё наудачу без возвращения извлекают по одному шару. Найти вероятность того, что красный шар появится раньше синего.
В урне находятся 2 красных, 3 синих и 2 зеленых шара. Из неё наудачу без возвращения извлекают по одному шару. Найти вероятность того, что красный шар появится раньше синего.
Обсуждение
13.05.2021, 21:19
общий
это ответ
Здравствуйте, KSIW2S!
При начальном составе шаров в урне вероятность вынуть первым красный шар составляет
При начальном составе шаров в урне вероятность вынуть первым зелёный шар тоже составляет
После этого в урне останется 
красных, 
синих и один зелёный шар. Тогда вероятность вынуть затем красный шар составляет 
То есть если первым вынут зелёный шар, то вероятность вынуть следующим красный шар равна 
Пусть, однако, наряду с первым и второй вынутый из урны шар оказался зелёным. Вероятность такого события равна
В результате в урне останется красных и синих шара. В таком случае вероятность вынуть затем красный шар составляет 
То есть если первые два вынутых шара были зелёными, то вероятность вынуть следующим красный шар равна 
Искомая вероятность равна
При начальном составе шаров в урне вероятность вынуть первым красный шар составляет
При начальном составе шаров в урне вероятность вынуть первым зелёный шар тоже составляет
После этого в урне останется красных, синих и один зелёный шар. Тогда вероятность вынуть затем красный шар составляет То есть если первым вынут зелёный шар, то вероятность вынуть следующим красный шар равна Пусть, однако, наряду с первым и второй вынутый из урны шар оказался зелёным. Вероятность такого события равна
В результате в урне останется красных и синих шара. В таком случае вероятность вынуть затем красный шар составляет То есть если первые два вынутых шара были зелёными, то вероятность вынуть следующим красный шар равна Искомая вероятность равна
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
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