Решебник по математике 8 класс. вероятность и статистика Высоцкий ФГОС Часть 2 Задание 199

\[\boxed{\mathbf{199.}}\]

\[Длина\ полуокружности:\]

\[L = \frac{\text{πR}}{2}.\]

\[Дуга\ AB = 180{^\circ}.\]

\[\textbf{а)}\ 90{^\circ} = \frac{1}{2} \cup AB;\]

\[P(X) = \frac{\frac{1}{2} \cdot \frac{\text{πR}}{2}}{\frac{\text{πR}}{2}} = \frac{1}{2} = 0,5.\]

\[\textbf{б)}\ \cup BC = 120{^\circ};\]

\[\cup AC = 180{^\circ} - 120{^\circ} = 60{^\circ};\]

\[P(X) = \frac{\frac{1}{3} \cdot \frac{\text{πR}}{2}}{\frac{\text{πR}}{2}} = \frac{1}{3}.\]

\[\textbf{в)}\ \cup CD = 60{^\circ} - 30{^\circ} = 30{^\circ};\]

\[30{^\circ} = \frac{1}{6} \cup AB;\]

\[P(X) = \frac{\frac{1}{6} \cdot \frac{\text{πR}}{2}}{\frac{\text{πR}}{2}} = \frac{1}{6}.\]