Schemat Bernoulliego
P_n(k)={n\choose k}\cdot p^k\cdot q^{n-k} wzór
k sukcesów w n próbach
a)
n=5
k=10
p=\frac{6}{10}
q=1-p=1-\frac{6}{10}=\frac{4}{10}
P(A)={5\choose 0}\cdot (\frac{6}{10})^0\cdot (\frac{4}{10})^{5-0}+{5\choose 1}\cdot (\frac{6}{10})^1\cdot (\frac{4}{10})^{5-1}+{5\choose 2}\cdot (\frac{6}{10})^2\cdot (\frac{4}{10})^{5-2}=
=1\cdot1\cdot(\frac{4}{10})^5+5\cdot\frac{6}{10}\cdot(\frac{4}{10})^4+\frac{3!\cdot4\cdot5}{3!*\not2^1}\cdot\frac{\not36^{18}}{100}\cdot (\frac{4}{10})^{3}=
(\frac{4}{10})^3\cdot(\frac{4^2}{100}+3*\frac{4^1}{10}+\frac{360}{100}\cdot1)=
=(\frac{4}{10})^3\cdot(\frac{16}{100}+\frac{12}{10}+\frac{360}{100})=
\frac{64}{1000}\cdot \frac{16+120+360}{100}=
=\frac{64*640}{10^5}=\frac{64\cdot 496}{10^5}=\frac{31744}{10^5}=0,31744
Odpowiedź:
0,31744