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Консультация № 190278
11.12.2016, 21:48
0.00 руб.
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1
Здравствуйте, уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Дан прямоугольник в системе координат (0;0), (0;1), (3;1), (3;0). Наудачу бросили точку (х;у) в прямоугольник. Какова вероятность, что координаты точки удовлетворяют неравенству у<x?
Заранее спасибо за ответы.
Дан прямоугольник в системе координат (0;0), (0;1), (3;1), (3;0). Наудачу бросили точку (х;у) в прямоугольник. Какова вероятность, что координаты точки удовлетворяют неравенству у<x?
Заранее спасибо за ответы.
Обсуждение
12.12.2016, 08:51
общий
это ответ
Здравствуйте, kainnord!
Воспользуемся геометрическим определением вероятности. Выполним рисунок.
Пусть
- событие, состоящее в том, что точка, брошенная в прямоугольник, попадёт в область 
Тогда вероятность 
этого события равна отношению площадей трапеции, окрашенной на рисунке в светло-синий цвет, и прямоугольника, то есть
Воспользуемся геометрическим определением вероятности. Выполним рисунок.
Пусть
- событие, состоящее в том, что точка, брошенная в прямоугольник, попадёт в область Тогда вероятность этого события равна отношению площадей трапеции, окрашенной на рисунке в светло-синий цвет, и прямоугольника, то есть
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
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