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Консультация № 176834
21.02.2010, 17:46
0.00 руб.
0
3
3
Доброго времени суток.
Нужна ваша помощь:В лифт 9этажнего здания на первом этаже зашло 3 человека,знаем что каждый из них с одинаковой вероятностью может выйти на любом этаже, начиная со второго ,определить какова вероятность того что все 3 человека выйдут на разных этажах. К ответу предоставить расчёты
Нужна ваша помощь:В лифт 9этажнего здания на первом этаже зашло 3 человека,знаем что каждый из них с одинаковой вероятностью может выйти на любом этаже, начиная со второго ,определить какова вероятность того что все 3 человека выйдут на разных этажах. К ответу предоставить расчёты
Обсуждение
21.02.2010, 18:08
общий
это ответ
Здравствуйте, Бабич Илья Александрович.
Первый может выйти на любом этаже. Вероятность, что второй не выйдет на том же этаже, 7/8. Вероятность, что третий не выйдет на двух предыдущих, 6/8.
7/8*6/8=7/8*3/4=21/32=65,625%
Первый может выйти на любом этаже. Вероятность, что второй не выйдет на том же этаже, 7/8. Вероятность, что третий не выйдет на двух предыдущих, 6/8.
7/8*6/8=7/8*3/4=21/32=65,625%
5
Спасибо большое,понял где ошибся когда сам делал
Неизвестный
21.02.2010, 18:11
общий
это ответ
Здравствуйте, Бабич Илья Александрович.
Каждый из 3-х человек может выйти на любом из 8ми этажей, значит общее число исходов равно 8^3. Нас интересуют случаи, когда все выходят на разных этажах, т.е. когда 1й человек может выйти на любом из 8 этажей, 2й - только на оставшихся 7-ми, и 3й - на оставшихся 6 этажах. Таких случаев ровно 8*7*6.
Искомая вероятность равна 8*7*6/(8^3) = 21/32
Каждый из 3-х человек может выйти на любом из 8ми этажей, значит общее число исходов равно 8^3. Нас интересуют случаи, когда все выходят на разных этажах, т.е. когда 1й человек может выйти на любом из 8 этажей, 2й - только на оставшихся 7-ми, и 3й - на оставшихся 6 этажах. Таких случаев ровно 8*7*6.
Искомая вероятность равна 8*7*6/(8^3) = 21/32
5
Спасибо за помощь
Неизвестный
21.02.2010, 22:48
общий
это ответ
Здравствуйте, Бабич Илья Александрович.
Вероятность выйти первого на любом этаже – 8/8, вероятность второго выйти на любом кроме того, на котором вышел первый – 7/8, вероятность третьего выйти на осташихся 6 этажах – 6/8.
P = 8/8 * 7/8 * 6/8 = 0,65625
Вероятность выйти первого на любом этаже – 8/8, вероятность второго выйти на любом кроме того, на котором вышел первый – 7/8, вероятность третьего выйти на осташихся 6 этажах – 6/8.
P = 8/8 * 7/8 * 6/8 = 0,65625
5
Спасибо за подсказку
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