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Консультация № 187564
08.10.2013, 22:26
79.10 руб.
0
2
2
Уважаемые эксперты! Пожалуйста, ответьте на вопрос: В первой урне 2 голубых и 6 красных шаров, во второй - 4 голубых и 2 красных. из первой урны наудачу переложили 2 шара во вторую, после чего из второй урны наудачу достали один шар. Какова вероятность того, что этот шар голубой? Заранее благодарен.
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Неизвестный
08.10.2013, 22:51
общий
это ответ
Здравствуйте, Тимофеев Алексей Валентинович!
Понятно, что из первой урны будет извлечено от 0 до 2 голубых шаров, и эти события образуют полную группу.
1) Оба извлеченных шара красные: вероятность 6/8 * 5/7=15/28
2) один извлеченный шар красный: вероятность 6/8 * 2 /7 + 2/8 *6/7=3/7
3) оба шара голубые: 2/8*1/7=2/56.
По формуле полной вероятности искомая вероятность равна 15/28*1/2+3/7*5/8+2/56*3/4=9/16.
Понятно, что из первой урны будет извлечено от 0 до 2 голубых шаров, и эти события образуют полную группу.
1) Оба извлеченных шара красные: вероятность 6/8 * 5/7=15/28
2) один извлеченный шар красный: вероятность 6/8 * 2 /7 + 2/8 *6/7=3/7
3) оба шара голубые: 2/8*1/7=2/56.
По формуле полной вероятности искомая вероятность равна 15/28*1/2+3/7*5/8+2/56*3/4=9/16.
5
08.10.2013, 22:53
общий
это ответ
Здравствуйте, Тимофеев Алексей Валентинович!
Рассмотрим следующие случайные события: A - шар из второй урны оказался голубым,
гипотезы:
В1 - во вторую урну переложили 2 голубых шара,
В2 - во вторую урну переложили 1 голубой и 1 красный шар,
В3 - во вторую урну переложили 2 красных шара,.
Подсчитаем вероятности гипотез, используя теорему умножения вероятностей зависимых событий и теорему сложения вероятностей несовместных событий:
Р(В1)=(2/8)*(1/7)=1/28,
Р(В2)=(2/8)*(6/7)+(6/8)*(2/7)=3/7,
Р(В3)=(6/8)*(5/7)=15/28.
Условные вероятности события А находим по классической формуле вероятности:
Р(А|В1)=6/(6+2)=3/4,
Р(А|В2)=5/(5+3)=5/8,
Р(А|В3)=4/(4+4)=1/2.
Полная вероятность события А:
Р(А)=Р(В1)[$183$]Р(А|В1)+Р(В2)[$183$]Р(А|В2)+Р(В3)[$183$]Р(А|В3)=(1/28)[$183$](3/4)+(3/7)[$183$](5/8)+(15/28)[$183$](1/2)=63/112.
Рассмотрим следующие случайные события: A - шар из второй урны оказался голубым,
гипотезы:
В1 - во вторую урну переложили 2 голубых шара,
В2 - во вторую урну переложили 1 голубой и 1 красный шар,
В3 - во вторую урну переложили 2 красных шара,.
Подсчитаем вероятности гипотез, используя теорему умножения вероятностей зависимых событий и теорему сложения вероятностей несовместных событий:
Р(В1)=(2/8)*(1/7)=1/28,
Р(В2)=(2/8)*(6/7)+(6/8)*(2/7)=3/7,
Р(В3)=(6/8)*(5/7)=15/28.
Условные вероятности события А находим по классической формуле вероятности:
Р(А|В1)=6/(6+2)=3/4,
Р(А|В2)=5/(5+3)=5/8,
Р(А|В3)=4/(4+4)=1/2.
Полная вероятность события А:
Р(А)=Р(В1)[$183$]Р(А|В1)+Р(В2)[$183$]Р(А|В2)+Р(В3)[$183$]Р(А|В3)=(1/28)[$183$](3/4)+(3/7)[$183$](5/8)+(15/28)[$183$](1/2)=63/112.
5
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