Question

Oblicz:
P=3/20+2/20*3/19+2/20*1/19*3/18

Answer 1

Odpowiedź:

[tex]\Large\boxed{P=\dfrac{1}{6}}[/tex]

Szczegółowe wyjaśnienie:

[tex]P=\dfrac{3}{20}+\dfrac{2}{20}\cdot \dfrac{3}{19}+\dfrac{2}{20}\cdot\dfrac{1}{19}\cdot\dfrac{3}{18}=\\[5]\dfrac{3}{20}\cdot\left(1+\dfrac{2}{19}+\dfrac{2}{19\cdot18}\right)=\\[5]\dfrac{3}{20}\cdot\left(1+\dfrac{2}{19}\cdot\left(1+\dfrac{1}{18}\right)\right)=\\[5]\dfrac{3}{20}\cdot\left(1+\dfrac{2}{{\not}19}\cdot\dfrac{{\not}19}{18}\right)=\\[5]\dfrac{3}{20}\cdot\left(1+\dfrac{2}{18}\right)=\\[5]\dfrac{3}{{\not}20}\cdot\dfrac{{\not}20}{18}=\dfrac{1}{6}[/tex]