Hi tmt!

Since you've posted in probability and statistics, are we talking about the intersection and union of chance events?

And the resulting probabilities?

If so, then the product rule states that if events $A$ and $B$ are

*independent*, that then $P(A\cap B)=P(A)P(B)$.

So it would be the product, not the subtraction. If they're not

*independent*, it becomes more complicated.

And the sum rule states that if events $A$ and $B$ are

*mutually exclusive*, that then $P(A\cup B)=P(A)+P(B)$.

So it would be the sum, and not the larger number.

However, we can already see in this case that the sum would be greater than $1$, which is not possible for probabilities, so $A$ and $B$ are definitely not

*mutually exclusive*. In that case we need the general sum rule $P(A\cup B)=P(A)+P(B)-P(A\cap B)$.