what probability formula should be used here? 
For a bill to come before the president of the United States, it must be passed by both the House of Representatives and the Senate. Assume that, of the bills presented to these two bodies, $60$ percent pass the House, $80$ percent pass the Senate, and $90$ percent pass at least one of the two. Calculate the probability that the next bill presented to the two groups will come before the president.

In the above problem, why can't we just multiply the probability of passing the bill by the House and Senate together to get the probability of the bill coming before the president?
like this:
\begin{align*}
P(\text{Senate,House}) & = P(\text{Senate})P(\text{House})\\
P(\text{Senate,House}) & = 0.6 \cdot 0.8
\end{align*}
I know the True answer is found this way:
$$P(\text{Senate or House})= P(\text{Senate})+ P(\text{House})-P(\text{Senate,House})$$
But I'm wondering why we can not just simply multiply the two probabilities to get the answer?
 A: Let $P(S)$ denote the probability that a bill passes the Senate; let $P(H)$ denote the probability that a bill passes the House of Representatives.  As you are aware,
$$P(H \cup S) = P(H) + P(S) - P(H \cap S)$$
Solving for $P(H \cap S)$ yields
$$P(H \cap S) = P(H) + P(S) - P(H \cup S)$$
Substituting $0.6$ for $P(H)$, $0.8$ for $P(S)$, and $0.9$ for $P(H \cup S)$ yields 
$$P(H \cap S) = 0.6 + 0.8 - 0.9 = 0.5$$

But I'm wondering why we can't just multiply the two probabilities to get the answer?

Well, 
$$P(H)P(S) = 0.6 \cdot 0.8 = 0.48 \neq 0.5 = P(H \cap S)$$
Clearly, multiplying the two probabilities does not produce the correct result.  You could multiply the two probabilities if the events were independent, in which case we would have 
$$P(H \cap S) = P(H)P(S)$$ 

Aren't [the] two events independent?  [The] probability of [a bill] passing the House and the Senate seems to be independent to me.

When two events are independent, the occurrence of one event does not affect the occurrence of the other. 
If both houses of Congress are controlled by the same party, they are more likely to agree on a bill.  If the houses of Congress are controlled by different parties, they are less likely to agree on a bill.  There is no reason to assume independence.
