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z)0vC=zlVg2A3n%`*um%3|Ije^f6W=V-5+hh`=1-c3zx~6HD_lxxJ3THKF?&Gtek;A`{Xb3x~v3HpW%PoZW)39`=wvsVBmW$#O>Es!p#Mr MALz8SlFCy55B=q??EnA( diff --git a/labs/lab1/res.typ b/labs/lab1/res.typ index 4317430..97d90f1 100644 --- a/labs/lab1/res.typ +++ b/labs/lab1/res.typ @@ -173,14 +173,46 @@ $ *3*. _Прибор содержит шесть однотипных микросхем, вероятность выхода из строя каждой в течение одного месяца равна $0.2$. Найти вероятность того, что в течение этого срока из строя выйдет не более половины микросхем._ -*Решение*: +*Решение*: Пусть $n = 6, space p = 0.2$, тогда нужно найти $P(X lt.eq 3)$. -*Ответ*: +По стандартной формуле получим: + +$ +P(X = k) = C_6^k dot 0.2^k dot 0.8^(6 - k) +$ + +Рассчитаем: + +$ +P(X lt.eq 3) = P(0) + P(1) + P(2) + P(3) +$ + +Опустив вычисления, получим: + +$ +P(X lt.eq 3) = 0.982 +$ + +*Ответ*: $0.982$. #line(length: 100%) *13*. Производится испытание на "самовозгорание" пяти телевизоров. Прогонка продолжается двое суток. За указанное время каждый из телевизоров перегревается и "самовозгорается" с вероятностью $0.1$. Найти вероятность того, что на момент окончания испытаний сгорит не более двух телевизоров. -*Решение*: +*Решение*: Пусть $n = 5, space p = 0.1$. Тогда нужно найти $P(X lt.eq 2)$. -*Ответ*: +$ +P(X = k) = C_5^k (0.1)^k (0.9)^(5 - k) +$ + +$ +P(X lt.eq 2) = P(0) + P(1) + P(2) +$ + +Опустив вычисления, получим: + +$ +P(X lt.eq 2) = 0.99144 +$ + +*Ответ*: $0.99144$.