Question

The table to the right lists probabilities for the corresponding numbers of girls
in three births. What is the random variable, what are its possible values, and
are its values numerical?
# of girls P(x)
0 0.125
1 0.375
2 0.375
3 0.125

Answer 1

A random variable is an outcome that we cannot predict before the experiment is performed.
For example, in the toss of a single fair six-sided die, the side (numbered 1 to 6) facing up is the random variable. Its possible values are {1,2,3,4,5,6}.

Answer 2

The number of girls born in 3 births is your random variable, it is not known and thus there can be either 1 girl, 2girls or 3 girls born in 3 consecutive births
It's possible values are, as you can see 0,1,2,3 from the table