Садовник принес две корзинки фруктов. В одной из них 3 яблока и 9 персиков, а в другой  — 12 яблок и 18 персиков. Хозяйка, не глядя, взяла из каждой корзинки по одному фрукту. Какова вероятность того, что она достала два яблока или два персика?

Для решения этой задачи нам нужно посчитать вероятность того, что хозяйка достала два яблока или два персика.

В первой корзинке всего 12 фруктов, из которых 3 яблока и 9 персиков. Вероятность достать яблоко из первой корзинки равна 3/12 = 1/4, а вероятность достать персик равна 9/12 = 3/4.

Аналогично, во второй корзинке всего 30 фруктов, из которых 12 яблок и 18 персиков. Вероятность достать яблоко из второй корзинки равна 12/30 = 2/5, а вероятность достать персик равна 18/30 = 3/5.

Теперь посчитаем вероятность того, что хозяйка достала два яблока: P(два яблока) = P(яблоко из первой корзинки) * P(яблоко из второй корзинки) = (1/4) * (2/5) = 1/10.

Аналогично, вероятность того, что хозяйка достала два персика: P(два персика) = P(персик из первой корзинки) * P(персик из второй корзинки) = (3/4) * (3/5) = 9/20.

Таким образом, общая вероятность того, что хозяйка достала два яблока или два персика, равна сумме вероятностей: P(два яблока или два персика) = P(два яблока) + P(два персика) = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 9/20 = 1/10 + 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