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Консультация № 173176
11.10.2009, 15:51
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Здравствуйте, уважаемые эксперты!
Заранее спасибо!
Медицинский тест на возможность вирусного заболевания дает следующие результаты:
1. Если проверяемый болен, то тест даст положительный результат с вероятностью 0.92.
2. Если проверяемый не болен, то тест может дать положительный результат с вероятностью 0.04.
Поскольку заболевание редкое, то ему подвержено только 0.1% населения. Предположим, что некоторому случайно выбранному человеку сделан анализ и получен положительный результат. Чему равна вероятность того, что человек действительно болен?
Заранее спасибо!
Медицинский тест на возможность вирусного заболевания дает следующие результаты:
1. Если проверяемый болен, то тест даст положительный результат с вероятностью 0.92.
2. Если проверяемый не болен, то тест может дать положительный результат с вероятностью 0.04.
Поскольку заболевание редкое, то ему подвержено только 0.1% населения. Предположим, что некоторому случайно выбранному человеку сделан анализ и получен положительный результат. Чему равна вероятность того, что человек действительно болен?
Обсуждение
Неизвестный
11.10.2009, 16:24
общий
это ответ
Здравствуйте, Волков Сергей Юриевич.
Событие A - проверяемый болен.
Событие B - проверяемый не болен
Событие C - тест дал положительный результат.
Тогда
P(C/A) = 0.92 - вероятность, что тест даст положительный результат, если проверяемый болен;
P(C/B) = 0.04 - вероятность, что тест даст положительный результат, если проверяемый не болен;
P(A) = 0.1%=0.001 - вероятность, что проверяемый болен.
P(B) = 1-P(A) = 0.999 - вероятность того, что проверяемый не болен.
По формуле Бейеса получаем
P(A/C)=P(A)*P(C/A)/(P(A)*P(C/A)+P(B)*P(C/B))*100% = 2.25%
Событие A - проверяемый болен.
Событие B - проверяемый не болен
Событие C - тест дал положительный результат.
Тогда
P(C/A) = 0.92 - вероятность, что тест даст положительный результат, если проверяемый болен;
P(C/B) = 0.04 - вероятность, что тест даст положительный результат, если проверяемый не болен;
P(A) = 0.1%=0.001 - вероятность, что проверяемый болен.
P(B) = 1-P(A) = 0.999 - вероятность того, что проверяемый не болен.
По формуле Бейеса получаем
P(A/C)=P(A)*P(C/A)/(P(A)*P(C/A)+P(B)*P(C/B))*100% = 2.25%
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