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Консультация № 202292
12.03.2022, 01:19
0.00 руб.
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Сколько раз нужно бросить пару игральных костей, чтобы с вероят- ностью, не меньшей 0,5, хотя бы один раз появилась сумма очков, равная 12?
Сколько раз нужно бросить пару игральных костей, чтобы с вероят- ностью, не меньшей 0,5, хотя бы один раз появилась сумма очков, равная 12?
Обсуждение
14.03.2022, 14:47
общий
это ответ
Здравствуйте, svrvsvrv!
Противоположным выпадению суммы очков, равной 12, хотя бы один раз, является отсутствие такой суммы при всех сделанных бросках двух игральных костей. Поэтому для решения задачи можно вычислить, сколько бросков пары игральных костей нужно сделать, чтобы с вероятностью, меньшей 0,5, ни разу не выпала сумма очков, равная 12.
Вероятность того, что при бросании пары игральных костей выпадет сумма очков, равная 12, составляет
а вероятность того, что выпадет другая сумма, составляет 
Вероятность того, что сумма, не равная 12, выпадет 
раз, составляет 
Решим неравенство 
Получим 
Следовательно, нужно бросить пару игральных костей не менее 
раз.
Противоположным выпадению суммы очков, равной 12, хотя бы один раз, является отсутствие такой суммы при всех сделанных бросках двух игральных костей. Поэтому для решения задачи можно вычислить, сколько бросков пары игральных костей нужно сделать, чтобы с вероятностью, меньшей 0,5, ни разу не выпала сумма очков, равная 12.
Вероятность того, что при бросании пары игральных костей выпадет сумма очков, равная 12, составляет
а вероятность того, что выпадет другая сумма, составляет Вероятность того, что сумма, не равная 12, выпадет раз, составляет Решим неравенство Получим Следовательно, нужно бросить пару игральных костей не менее раз.
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
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