Question

If a family has $3$ children.If independent enter $1$ else enter $0$.

Answer 1

We have the equiprobable space $S=\{bbb,bbg,bgb,bgg,gbb,gbg,ggb,ggg\}$
here $A=\{bbg,bgb,bgg,gbb,gbg,ggb\}$ So$=P\left(A\right)=\frac{6}{8}=\frac{3}{4}$
$B=\{bgg,gbg,ggb,ggg\}$ and so$=P\left(B\right)=\frac{4}{8}=\frac{1}{2}$
$A\cap B=\{bgg.gbg,ggb\}$ and so $P(A\cap B)=\frac{3}{8}$
Since $P\left(A\right).P\left(B\right)=\frac{3}{4}\times \frac{1}{2}=\frac{3}{8}=P(A\cap B)$
Thus, $A$ and $B$ are independent