Question

A family has two children. If B represents a boy and G represents a girl, the set of outcomes for the possible genders of the children is S = {BB, BG, GB, GG}, with the oldest child listed first in each pair. Let X represent the number of times G occurs. Which of the following is the probability distribution, PX(x)?

Answer 1

Answer: P(X=0) = 1/4, P(X=1)=1/2 and P(X=2)= 1/4.

Explanation:

Since, the possible genders of the children is S = {BB, BG, GB, GG}

Here, Let X represent the number of times G occurs.

Thus, when there is no girl

Possible arrangement = {BB}

Then P(X=0) = 1/4

When there is one girl,

Then possible arrangement = { BG, GB}

Thus P(X=1)= 2/4

⇒ P(X=1)=1/2

When there is 2 girls,

Then possible arrangement = {GG}

Thus P(X=2)= 1/4