Question 1152662

a) {{{x = 2}}}

 using the binomial formula

{{{P(x)= nCx*pi^x(1-pi)^(n-x)}}} where {{{x=2}}}, {{{n = 5}}} and {{{pi= .25}}}

{{{P(2)= 5C2*pi^2(1-pi)^(5-2)}}}

{{{P(2)= 5C2*.25^2(1-.25)^3}}}


{{{5C2=5!/(2!(5-2)!)=(5*4*3*2*1)/(2*3*2*1)=10}}}

{{{P(2)= 10*.25^2(.75)^3}}}

{{{P(2)= 0.2637}}}


b) {{{x = 3}}}

{{{P(x)= nCx*pi^x(1-pi)^(n-x)}}} where{{{ x=3}}}, {{{n = 5}}} and {{{pi=.25}}}

{{{P(3)= 5C3*pi^2(1-pi)^(5-3)}}}

{{{P(3)= 5C3*.25^2(1-.25)^2}}}

{{{5C3=5!/(3!(5-3)!)=(5*4*3*2*1)/(2*3*2*1)=10}}}

{{{P(3)= 10*.25^2(.75)^2}}}

{{{P(3)= 0.3516}}}