Решебник по математике 8 класс. вероятность и статистика Высоцкий ФГОС Часть 2 Задание 239

\[\boxed{\mathbf{239.}}\]

\[p = q = \frac{1}{2}.\]

\[\textbf{а)}\ C_{5}^{3} \cdot \left( \frac{1}{2} \right)^{5} = \frac{5!}{3!2!} \cdot \frac{1}{2^{5}} =\]

\[= \frac{4 \cdot 5}{2 \cdot 32} = \frac{5}{16} \approx 0,313.\]

\[= \frac{1}{2^{5}} \cdot \left( 2 \cdot C_{5}^{2} + C_{5}^{4} \right) =\]

\[= \frac{1}{32} \cdot \left( \frac{2 \cdot 5!}{3!2!} + \frac{5!}{4!} \right) =\]

\[= \frac{1}{32} \cdot (4 \cdot 5 + 5) = \frac{1}{32} \cdot 25 =\]

\[= \frac{25}{32} \approx 0,781.\]

\[\textbf{в)}\ \frac{1}{2^{5}} \cdot \left( C_{5}^{1} + C_{5}^{3} \right) =\]

\[= \frac{1}{32} \cdot \left( 5 + \frac{5!}{3!2!} \right) =\]

\[= \frac{1}{32} \cdot (5 + 10) = \frac{15}{32} \approx 0,469.\]

\[\textbf{г)}\ \frac{1}{2^{5}} \cdot \left( C_{5}^{1} + C_{5}^{3} + C_{5}^{5} \right) =\]

\[= \frac{1}{32} \cdot (5 + 10 + 1) = \frac{16}{32} = 0,5.\]