In a family of 6 children, what is the probability that there will be exactly 2 boys? You should assume that the probability of having a boy always equals that of having a girl
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Let Y denote the # of boys
Then Y~Binomial(n=6,p=0.5)
a.
P(Y=2)=6C2 (0.5)^2 (1-0.5)^4
=0.234375
b.
E(Y)=np=6*0.5=3
c.
E(6-Y)=6-np=6-3=3
Then Y~Binomial(n=6,p=0.5)
a.
P(Y=2)=6C2 (0.5)^2 (1-0.5)^4
=0.234375
b.
E(Y)=np=6*0.5=3
c.
E(6-Y)=6-np=6-3=3