Suppose that a $4-$bit string is chosen uniformly at random.

What is the probability that the sum of its bits is exactly $2?$

Explain your answer.

Tips: A uniform distribution implies that the probability for each $4-$bit string to appear is $1/16.$

As a few examples, we have:

The string $(0000)$ : the sum of its bits is $0.$ The string $(0001)$ : the sum of its bits is $1.$

The string $(0010)$ : the sum of its bits is $1.$ The string $(1010)$ : the sum of its bits is $2.$

The string $(0111)$ : the sum of its bits is $3.$ The string $(1111)$ : the sum of its bits is $4$