Afamily 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)?

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

Step-by-step 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