How to Calculate the Probability (P(x)) in a Probability Distribution

I am working on statistics, and I am wondering how they got the values for the probability of having x number of girls in 4 births? I thought I understood this when reading the textbook, but even after going over it again, I am not too sure I understand it clearly. The way I understood P(x) to mean is that we can calculate the probability of a [discrete] random variable (in this case, the number of girls born out of four births). Although I know we can take the probability of an event happening to the nth value, I am not overly sure how they got the .063 on either side of the table below. From my understanding, wouldn't P(x) be .125 for both 0 girls and 4 girls?

Any help is appreciated! Thank you

They are using classic probability model for the problem. If $\Omega$ is the set of all possible vectors of 4 births, the $\Omega=\{(b_1,b_2,b_3,b_4): b_i\in\{girl, boy\}\}$, so there are $2^4=16$ possible results for 4 births, out of wich only $(boy,boy,boy,boy)$ corresponds to $x=0$, then $p(0)=1/16 =0.625$

A similar reasoning is used to compute the probability $p(x)$ of any $x$.