Вопрос школьника
Вероятность появления события А в каждом из 625 испытаний равна 0,64. Найти вероятность того, что событие А в этих испытаниях появиться ровно 415 раз.
Ответ от учителя
Для решения данной задачи необходимо воспользоваться формулой Бернулли, которая позволяет вычислить вероятность того, что в серии из n независимых испытаний событие А произойдет k раз:
P(k) = C(n, k) * p^k * (1-p)^(n-k),
где C(n, k) — число сочетаний из n по k, p — вероятность появления события А в каждом из n испытаний, (1-p) — вероятность того, что событие А не произойдет в каждом из n испытаний.
В данной задаче n = 625, p = 0,64, k = 415. Подставляя значения в формулу, получаем:
P(415) = C(625, 415) * 0,64^415 * (1-0,64)^(625-415) ≈ 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