The answer choices are very spread apart, so it's likely that you'll be able to estimate when solving this problem. The question asks for the probability that the picnic will take place. If it doesn't rain, then the picnic will still take place; if it does rain, then there's only a 50% chance that the picnic will still take place. And there's a 30% chance of rain.
Think through the possible ways in which the picnic could still be held:
(1) It doesn't rain.
OR
(2) It does rain but the picnic is not canceled.
If either of those things happens, then the picnic will be held. You have the information needed to calculate the respective probabilities of the two scenarios. The OR indicates that you'll add the two probabilities together once you've found them.
(1) It doesn't rain. There's a 30% chance that it will rain, so there's a 70% chance that it won't rain. So there's at least a 70% chance that the picnic will be held. Eliminate answers (A), (B), and (C).
And then there's still another scenario that could result in the picnic being held, so the probability has to be something greater than 70%. Only one answer is greater than 70%, so pick it.
The correct answer is (E).
Here's how to do the rest of the calculation, just in case you need to do so on a different problem:
(2) It does rain but the picnic is not canceled. This scenario is Rain AND Not Canceled. There's a 30% chance it will rain and a 50% chance that the picnic will still be held even if it does rain. The AND tells you to multiply these two probabilities together. You start with a 30% chance and then you're going to take 50%—or half—of that. Half of 30% is 15%, so there's a 15% chance that it will rain AND the picnic won't be canceled.
Add the probabilities from the two scenarios together: 70% + 15% = 85%.
