Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 567

\[1)\ На\ первой\ кости\ разные\ числа:\]

\[P(A) = \frac{21}{28} = \frac{3}{4};\text{\ \ \ }\]

\[P\left( B\text{/}A \right) = \frac{12}{28 - 1} = \frac{12}{27} = \frac{4}{9};\]

\[P\left( \text{AB} \right) = P(A) \bullet P\left( B\text{/}A \right) =\]

\[= \frac{3}{4} \bullet \frac{4}{9} = \frac{3}{9} = \frac{1}{3}.\]

\[2)\ На\ первой\ кости\ равные\ числа:\]

\[P(C) = \frac{7}{28} = \frac{1}{4};\text{\ \ \ }\]

\[P\left( D\text{/}C \right) = \frac{6}{28 - 1} = \frac{6}{27} = \frac{2}{9};\]

\[P\left( \text{CD} \right) = P(C) \bullet P\left( D\text{/}C \right) =\]

\[= \frac{1}{4} \bullet \frac{2}{9} = \frac{1}{2 \bullet 9} = \frac{1}{18}.\]

\[3)\ Общая\ вероятность:\]

\[P(AB + CD) = P\left( \text{AB} \right) + P\left( \text{CD} \right) =\]

\[= \frac{1}{3} + \frac{1}{18} = \frac{7}{18}.\]

\[Ответ:\ \ \frac{7}{18}.\]