Since the probabilities are mutually exclusive, we know that they don't interact with eachother. If I were to contextualize this, say two events that depend on eachother were a venn diagram. We would see that to find P(A and B) or P(A or B) would require you to find the intersection between the two. In this case, the probabilities would be akin to a spinner. We see that the spinner has a few sections, A and B being part of them. P(A or B) would be the probability of picking either section, which would just be P(A) or P(B) while P(A and B) would be the product of the two sections based on the multiplication rule.
So, using this newfound information we can say that P(E or F) = P(E)+P(F)=.30+.45=.75