Question

Suppose a random selected family has 3 children. Define X to be the number of boys in the family, X = 0,1,2, and 3. Write the sample space, construct a probability distribution in table form, and make histogram.

Answer 1

Sample space: X = {0,1,2,3}

X ~ Bin(3, 0.5)

$P(X=0)={3 \choose 0}*({\frac 1 2})^3={\frac 1 8}$

$P(X=1)={3 \choose 1}*({\frac 1 2})^3={\frac 3 8}$

$P(X=0)={3 \choose 2}*({\frac 1 2})^3={\frac 3 8}$

$P(X=0)={3 \choose 0}*({\frac 1 2})^3={\frac 1 8}$