On the school debate team, $6$ out of the $14$ girls are seniors and $9$ of the $20$ boys are seniors. What is the probability that either a girl or a senior would randomly be selected to argue a position?
Let $G$ be the number of girls and $S$ the number of seniors. Then $$P(G \cup S) = P(G) + P(S) - P(G \cap S)$$ I don't know if I did this right or not.
So $$P(G \cup S) = (14/34) + (1/15) - (6/14)$$
Because there are $34$ total students and the chances of it being girls are $14$ over $35$, the chances of it being senior are $1$ over $15$ since $9 + 6 = 15$ and the chance of being senior is $1/15$.
I think I got $6/14$ because $P(S \cap G)$ would be $6/14$ because that's intersecting right? Did I do this right? How would I go on to solve this?