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)?

To determine the probability, the formula is by number of successful outcomes divided by number of possible outcomes. The number of possible outcomes in this problem is 4.

So to compute the probability distribution:

The number of times that 0 G appeared is 0.25 which is represented by BB which is 1/4.
The number of times that 1 G appeared is .5 which is represented by BG and GB which is 2/4.
The number of times that 2 G appeared is .25 which is represented by GG which is 1/4.

The probability distribution will look like this:
X       Px(x)
0         .25
1          .5
2         .25