A low-pressure weather system is approaching Plainville; rainfall resu

I marked the answer as C reason being "If I know the percentage of thunderstorms that result from low pressure weather system, that helps with finding the probability." Because the argument mentions thunderstorms sometimes results from low pressure systems and not always

Can someone please explain why the answer is not C?

sssanskaar

C is working in the wrong direction. We're trying to go from what we know (low-pressure system) to what the question asks about (chance of thundershower). So we need to know how likely it is that when we have a low-pressure system, we will get a thundershower. We already know that we're likely to have rain, but we don't know how likely the rain is to turn into a thundershower. B gives us the probability we need.

C, meanwhile, would only be useful if we KNEW we had a thundershower and wanted to figure out the cause. Then we might wonder how often thundershowers are caused by low-pressure systems vs. something else.

As a comparison, imagine that someone is drinking too much wine, and I suggest that they will feel sick the next day. To assess whether I'm right, it would be helpful to know how often people who drink too much wine feel sick the next day. It would not help to know how often people feel sick have drunk too much wine. Maybe most sickness is caused by other things (disease, other alcoholic beverages, etc.), but that doesn't do anything to change whether the wine would make us sick. If it did, one could avoid illness by drinking only very rare drinks: "Only a very tiny percentage of sick people became sick from drinking this vintage Albanian wine, so surely it will not make me sick."

Thanks DmitryFarber for explaining it in much simpler terms! It is now clear to me. I think I had missed one very important part that the rain and the thundershowers are not mutually exclusive sets. I had thought that these two are different things altogether.
As always, I am now clear in my understanding after reading your wonderful explanation. A heartfelt thank you!

I'm glad to help! I can see how the interpretation you were using made this a tough one. If we read "thundershower" to mean some kind of rain shower, then "thundershowers" must be a subset of "rainfall." If we were looking for something else, such as earthquakes, then B would look very odd--why would some rainfall also be earthquakes?--but it would still be useful to know this information. That means B is a great clue--"Oh, thundershowers can be a kind of rainfall?"--that may prompt us to question our assumptions and look at the problem differently. C would still not work, even if we were talking about earthquakes, for the same reasons I cited earlier. We still wouldn't know how likely it would be to have an earthquake when low-pressure systems came around.

Hi Buddy,
Thanks for your explanation. I get why C is wrong, but I still don't get why B is right. (I picked B as my answer choice FWIW, but I wasn't fond of it. It just seemed best of the worst choices)
Here's what I think:
Question: What is the probability that Plainville will have a thundershower soon?
What are we told already?
A low-pressure weather system is approaching Plainville; rainfall results from about 70 percent of such systems in the Plainville area - great info. Now we just need to figure out what percentage of such rainfall (i.e. rainfall resulting from low-pressure weather system, NOT just ANY RAINFALL) results in thundershowers. It is quite possible that low-pressure rainfalls never result in thundershowers (or they always result in thundershowers). We just dont know.

Moreover, the current season, spring, is the time of year in which thundershowers, which sometimes result from low-pressure systems, are most likely to occur in Plainville - OK good to know, but so what? This doesn't help us to answer the question. Spring is the time when thundershowers are likely. We need to know "given a low pressure system is approaching, how probable is it that it's going to result in a thundershower. Maybe the spring season alters that probability because it brings with it more low pressure systems, but that's irrelevant once we are there there already is a low pressure system. Moreover, there might be other types of rainfall in spring, not caused by low-pressure systems. So, we can ignore this statement.

So, just to recap, what do we need to find out?
what percentage of low-pressure system induced rainfall result in thundershowers


This isn't really what we are looking for. Sure it mentions a percentage of some rainfall, but not the kind we were looking for.
We need P(thundershower soon) = P(low-pressure) x P(thundershower caused by low-pressure)
We are given P(low-pressure) = 0.7, we aren't given P(thundershower caused by low-pressure)
Alternately, we can calculate it as follows:
P(thundershower soon) = P(rainfall in spring) x P(spring rainfall that is thundershower)
option B gives us the 2nd term of the equation, but not the first one.

We know
1. 70% of the time, a low preassure system results in rainfall over Plainville
2. We know that during the current season, Spring, Thundershowers which Sometimes Result from Low preassure systems, are Most likely to occur in Plainville

Now we don't need to get stuck up in clarifying precisely what the data of 'sometimes' or 'most likely' is supposed to mean, so we can eliminate the options that are committed to resolve this ambiguity. Instead, we must take this information at face value and pick the option that bridges the two TOGETHER.

If we know, Rainfall from LP system is likely, and we know that thunderstorms are also likely but only sometimes from LP system then we simply need to see what percent of rainfalls end up as thunderstorms to conveniently relate the data and achieve a conclusion.

If this was a response to my last comment/question, I still don’t get it
My point was:
P(a) = P(a/b) * P(b)
Also,
P(a) = P(a/c) * P(c)

Were given, P(a/b) and P(c). We can’t find P(a) from that information

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