Events A and B are mutually exclusive, with P(A) = 0.3 and P(B) = 0.45. What is P(A or B)?

Mutually exclusive events cannot occur together, so $P(A\text{ and }B)=0$. The addition rule simplifies to $P(A\text{ or }B)=P(A)+P(B)=0.3+0.45=0.75$, choice G. Choice F ($0.135$) multiplies the probabilities, which applies to independent events and would give $P(A\text{ and }B)$. Choice H ($0.15$) subtracts them. Choice J ($1.0$) would mean the two events together cover every outcome, which is not stated. The probability of either event must be at least as large as each single probability, and $0.75$ is larger than both $0.3$ and $0.45$.