Вопрос школьника
Вероятность найти белый гриб среди прочих равна 1/4. Какова вероятность того, что: а) среди 300 грибов белых будет 75; б) белых грибов будет не менее 50 и не более 100?
Ответ от учителя
а) Для решения этой задачи воспользуемся биномиальным распределением. Пусть p — вероятность найти белый гриб, тогда вероятность найти не белый гриб равна q = 1 — p. Тогда вероятность того, что среди 300 грибов будет 75 белых, равна:
P(X = 75) = C(300, 75) * p^75 * q^225
где C(300, 75) — число сочетаний из 300 грибов по 75 белых. Подставляя значения, получаем:
P(X = 75) = C(300, 75) * (1/4)^75 * (3/4)^225 ≈ 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