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Доброго времени суток. Возникли сложности с парой задач по теории вероятности: 1. Колода из 52 карт разделена на 2 равные части. Как найти вероятность того, что в одной половине будут все короли, а в другой все тузы? 2. В стойке 10 винтовок, из которых 6 снабжены оптическим прицелом. Вероятность того что стрелок поразит мишень из винтовки с оптическим прицелом составляет 0,8, а из винтовки без оптического прицела 0,6. Из двух винтовок, случайно выбранных из стойки, выстрелили по мишени, допустив один промах. Какова вероятность что выстрелы были произведены из винтовок без оптического прицела?
1. Колода из 52 карт разделена на 2 равные части. Как найти вероятность того, что в одной половине будут все короли, а в другой все тузы?
Пусть -- событие, состоящее в том, что в одной половине колоды находятся четыре короля, а в другой -- 4 туза. Это событие может состояться двумя равновероятными способами: 1) в "первой" половине будут 4 короля, а во "второй" -- 4 туза; 2) в "первой" половине будут 4 туза, а во "второй" -- 4 короля. Рассмотрим первый из указанных способов. Общее количество элементарных исходов равно количество благоприятных исходов При этом вероятность события составляет
При втором способе тоже Следовательно, искомая вероятность составляет
Если же половины колоды различать не нужно, то вероятность, соответственно, в два раза меньше.
5
Спасибо что подробно расписали сам процесс формирования решения задачи, теперь стало понятнее что от куда растет.
Об авторе:
Facta loquuntur.
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elleron 
-- событие, состоящее в том, что в одной половине колоды находятся четыре короля, а в другой -- 4 туза. Это событие может состояться двумя равновероятными способами: 1) в "первой" половине будут 4 короля, а во "второй" -- 4 туза; 2) в "первой" половине будут 4 туза, а во "второй" -- 4 короля. Рассмотрим первый из указанных способов. Общее количество элементарных исходов равно 
количество благоприятных исходов 
При этом вероятность события 
Следовательно, искомая вероятность составляет