Answer to Question #315648 in Statistics and Probability for temam

Question

. Let B be the number of boys in a family of 4 children. Construct a probability distribution of the random variable x. Construct a probability histogram 

Answer 1

Let probability of boy or girl is equal 0.5. 1 boy from 4 or 1 girl from 4 we can choose for 4 ways ($C_4^1=\frac{4!}{1!3!}=4)$ . And 2 boys from 4 we can choose for 6 ways ($C_4^2=\frac{4!}{2!2!}=6$ .

p- probability of boy ,equal 0.5

q - probability of girl, equal 0.5

$P(0)=q^4=0.5^4=0.0625$

$P(1)=4q^3p=4(0.5)^4=0.25$

$P(2)=6p^2q^2=6(0.5)^4=0.375$

$P(3)=4pq^3=4(0.5)^4=0.25$

$P(4)=p^4=0.0625$