Question 1153298

let {{{x}}} denote the number of girls in {{{n=4}}} independent births, where each has a probability {{{p-0.5}}}

we denote this by

{{{X}}}~binomial({{{n=4}}},{{{p=0.5}}})


probability of {{{x}}} number of girls is:


{{{P(X=x)=nCx*p^x*(1-p)^(n-x)}}}where {{{nCx=n!/(x!(n-x)!)}}}

{{{P(X=x)=(n!/(x!(n-x)!))*p^x*(1-p)^(n-x) }}}

{{{P(X=3)}}}, {{{n=4}}}, {{{p=0.5}}}

{{{P(X=3)=(4!/(3!(4-3)!))*0.5^3*(1-0.5)^(4-3)}}} 

{{{P(X=3)=(4!/(3!(1)))*0.5^3*(0.5)^(1) }}}

{{{P(X=3)=(4*3*2/(3*2))*0.125*0.5}}}

{{{P(X=3)=4*0.0625}}}

{{{P(X=3)=0.25}}}