Question

Let B be the number of boys in a family of 4 children

a) construct the probability distribution for the random variable B.

Answer 1

b = boys

g = girls

Sample space -{ bbbb,bbbg,bbgb,bbgg,bgbb,bgbg,bggb,bggg,gbbb,gbbg,gbgb,gbgg,ggbb,ggbg,gggb,gggg}

The possible outcomes for B are $0, 1, 2,3,4.$

$P(X=0)=\dfrac{1}{16}\\[9pt] P(X=1)=\dfrac{4}{16}=\dfrac{1}{4}\\[9pt] P(X=2)=\dfrac{6}{16}=\dfrac{3}{8}\\[9pt] P(X=3)=\dfrac{4}{16}=\dfrac{1}{4}\\[9pt] P(X=4)=\dfrac{1}{16}$

The probability distribution of B is-