The addition rule by counting

You will check the addition rule on a made-up survey of names, then write the rule itself and the complement rule as functions.

The idea. A list of names can stand for a group. A name in both lists is in the overlap. The addition rule is $P(A \cup B) = P(A) + P(B) - P(A \cap B)$, and the complement rule is $P(\text{not } A) = 1 - P(A)$.

Your tasks.

1. Finish in_both(group_a, group_b). Return a list of the names that are in both lists.
2. Finish p_union(pa, pb, pab). Return $P(A \cup B)$ from the three probabilities.
3. Finish p_neither(pa, pb, pab). Return the probability that neither event happens.