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Консультация № 195768
31.05.2019, 13:55
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Здравствуйте! У меня возникли сложности с таким вопросом:
На пяти карточках написаны цифры от 1 до 5. Друг за другом вытаскивают три карточки и в порядке поступления записывают число. Вероятность какого события выше: – «число меньше 450» или «число больше 200»?
На пяти карточках написаны цифры от 1 до 5. Друг за другом вытаскивают три карточки и в порядке поступления записывают число. Вероятность какого события выше: – «число меньше 450» или «число больше 200»?
Обсуждение
02.06.2019, 12:50
общий
это ответ
Здравствуйте, Анна Витальевна!
Количество n чисел, которые могут быть результатом рассматриваемого опыта, равно количеству размещений из пяти элементов по три, то есть n=5*(5-1)*(5-3+1)=5*4*3=60, согласно формуле (1) [1, с. 441].
Числами, которые больше, чем 450, являются 451, 452, 453, 512, 513, 514, 521, 523, 524, 531, 532, 534; всего 12 чисел. Поэтому количество чисел, которые меньше, чем 450, равно m1=60-12=48, а вероятность события "число меньше 450", согласно формуле (1) [1, с. 452], равна p1=m2/n=48/60=4/5=0,8.
Числами, которые меньше, чем 200, являются 123, 124, 125, 132, 134, 135, 142, 143, 145, 152, 153, 154; всего 12 чисел. Поэтому количество чисел, которые больше, чем 200, составляет m2=60-12=48, а вероятность события "число больше 200" равна p2=m2/n=48/60=4/5=0,8.
Вероятности обоих событий оказались одинаковыми.
Литература
1. Цыпкин А. Г., Пинский А. И. Справочник по методам решения задач по математике для средней школы. -- М.: Наука, 1989. -- 576 с.
Количество n чисел, которые могут быть результатом рассматриваемого опыта, равно количеству размещений из пяти элементов по три, то есть n=5*(5-1)*(5-3+1)=5*4*3=60, согласно формуле (1) [1, с. 441].
Числами, которые больше, чем 450, являются 451, 452, 453, 512, 513, 514, 521, 523, 524, 531, 532, 534; всего 12 чисел. Поэтому количество чисел, которые меньше, чем 450, равно m1=60-12=48, а вероятность события "число меньше 450", согласно формуле (1) [1, с. 452], равна p1=m2/n=48/60=4/5=0,8.
Числами, которые меньше, чем 200, являются 123, 124, 125, 132, 134, 135, 142, 143, 145, 152, 153, 154; всего 12 чисел. Поэтому количество чисел, которые больше, чем 200, составляет m2=60-12=48, а вероятность события "число больше 200" равна p2=m2/n=48/60=4/5=0,8.
Вероятности обоих событий оказались одинаковыми.
Литература
1. Цыпкин А. Г., Пинский А. И. Справочник по методам решения задач по математике для средней школы. -- М.: Наука, 1989. -- 576 с.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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