Question

findt he probability of at least 2 girls in 7 births. assume that male and female births are equally likely and that the births are independent events. help. thanks

Answer 1

\[\huge \frac{ 15 }{ 16 }\]

Answer 2

binomial problem!!! :)

Answer 3

Using the binomial distribution find the probability of exactly 0 female births and exactly 1 female birth and add these two values. Then subtract that sum from 1 to find the required probability.
\[P(0\ girls)=\left(\begin{matrix}7 \\ 0\end{matrix}\right)(\frac{1}{2})^{0}\times (\frac{1}{2})^{7}=\frac{1}{128}\]
\[P(1\ girl)=\left(\begin{matrix}7 \\ 1\end{matrix}\right)(\frac{1}{2})^{1}\times (\frac{1}{2})^{6}=\frac{7}{128}\]
\[P(0\ girls)+P(1\ girl)=\frac{1}{128}+\frac{7}{128}=\frac{1}{16}\]
\[P(at\ least\ 2\ girls)=1-\frac{1}{16}\]