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[Pop Quiz] If the Chance of Rain is 50% in the Morning and 50% After Noon, what's the Chance for the Day?

  • 102

[Pop Quiz] If the Chance of Rain is 50% in the Morning and 50% after Noon, what's the Chance Overall?

Replies • 16

50$, easy men give something harded


AlienGOD9853 sagte:

50$, easy men give something harded

[updated] 50%, 100% and "Impossible to tell" are wrong answers.

The solution has been posted on the second page. Less than 13 % got it right, with this small percentage continuing to decrease!?  This has been the entire point to show that, combining chances is tricky and basically impossible to guess correctly without knowing how to actually do it. 

edited

We cant know overall, without knowing "night" chances


237636

edited

In the way you put it, it's 50% in the morning AND [Meaning it's not related] 50% after noon. So, it's 50%.

If you throw a coin, the chance to get face/tails it's 50%. If you throw it again, it's 50% again, no correlation.

To have the effect you want, you should say something like "50% in the morning plus 50% more after noon". But that's just like, my opinion, man


the answer is zero that and you have provided us with zero infor, we dont have factors of wind high and low pressures and so on. we dont have a time of year ,location normal weather stuff like rainy seasons.


pizurk sagte:

In the way you put it, it's 50% in the morning AND [Meaning it's not related] 50% after noon. So, it's 50%.

If you throw a coin, the chance to get face/tails it's 50%. If you throw it again, it's 50% again, no correlation.

To have the effect you want, you should say something like "50% in the morning plus 50% more after noon". But that's just like, my opinion, man

AND is the same as PLUS. It is a sum, a coming together, a total, overall resulting, The difficulty is to ascribe a probability to a combined result. This is how chance of precipitation is presented if you check the weather online. It will have the chance for the day, as well as the same thing broken down into intervals (like 3 or 6 hours).

Please don't shoot the messenger. People like to criticize polls, phrasing, polling methods, bias etc. But this is just a humble multiple choice quiz. Asking people do do math is perhaps overly demanding, but participation is voluntary. Thank you, to everybody who participated. As far as I know, the voting is anonymous.

 

edited

It's 50%. If your definition of day here is just morning and afternoon, then one can argue that morning represents 1/2 of the day and afternoon the other 1/2.

Put into an equation: 0.5(1/2) + 0.5(1/2) = 0.5.

It doesn't matter if it rained twice during the day, one in the morning and one in the afternoon. The chances of rainfall on that day is still the average of both predictions.

Just to add, I don't agree on the coin flip analogy above. The reason coin flips are 50% is because you only have two possible outcomes, heads or tails, hence the 50% chance. No matter how many flips you do, there will only be two outcomes. So, in relation to the original post, unless we're only talking about if it rained or not for the day and not the probability of it raining, then the coin flip example is a totally different subject.

For this weather thing, forecasts aren't really simply talking about that though. Let's try a less confusing example, let's say 30% in the morning and 40% in the afternoon. 0.3(1/2) + 0.4(1/2) = 0.35 or 35% chance of rainfall for the day.

However, if you're looking for an accurate calculation for the chance of rainfall, then you're SOL. Weather predictions like this are subjective and will differ with each meteorologist.

So, if your additional argument is "because you have additonal chance in the afternoon, it can only increase. If you buy a second lottery ticket, your chances have to improve, right?" then don't you think that the afternoon prediction already includes the effects of the morning's prediction? And even so, what if it already rained in the morning? Then, it only decreases the chance of it raining in the afternoon. Or it could last the whole day. And we're not even accounting for the areas in which the rainfall happened or did not happen (this is included in the Probabilty of Precipitation equation).

So, in reality, this question is just not possible to actually answer if we're sternly going with the chance of rainfall narrative. We don't have the complete, or even enough, set of variables to actually compute for the probability here. I mean unless we're just going with will it rain or not, then that's always 1/2 or 50%. We're just going by the given 50% probabilty in the morning and 50% in the afternoon. So, all we can really do is average the two probabilities we've been presented.


NadineR said:

 If your definition of day here is just morning and afternoon, then one can argue that morning represents 1/2 of the day and afternoon the other 1/2.

The relevant and sufficient variables hiding in the text are: 2 possible outcomes (Rain/Dry) in 2 separate events (am/pm). They need to be combined, in a way that probability keeps increasing without spilling over 100%. I prefer the weather analogy for its practicality, but coins are fine or the lottery or loot boxes.

Your prediction only makes sense if the person actually arrived during the crucial day at noon. Probabilities are real, objective and consistent (always adding up to an exact 100%), however they only exist looking to the future. In the present they manifest as a random event. And looking to the past you see data/events that form a probabilistic pattern.

The chance for a coin toss does remain 50% if you move from one throw to the next, but if you look and calculate 2 or more (n) throws ahead. Then the number of possible outcomes becomes 2n, and stops being just "It either rains or it doesn't. Heads or Tails." The thing that trips people up is that there is a way to add probabilities intuitively, but it gets complicated and impractical quickly. Schools teach to map out all possible outcomes and add the rainy ones, just like you have attempted and there is a third "backwards" way that calculates the simpler chance of the opposite event occurring.

This really isn't a trick question, it's a bit cheeky because the obvious replies, can't possibly be right on second thought. People don't trust logic even though it could lead one to the right answer by excluding the wrong ones, without actually doing any multiplications.

I'm working on a comprehensive list, but if somebody likes to post a correct solution in the meantime...


However, "50% chance of rain" doesn't actually mean there's a 50/50 chance of it raining.  Probability of Precipitation has a specific calculation, and it's partly up to how a meteorologist feels (like a lot of weather forcasting).

From https://www.weather.gov/ffc/pop:

Mathematically, PoP is defined as follows:

PoP = C x A where "C" = the confidence that precipitation will occur somewhere in the forecast area, and where "A" = the percent of the area that will receive measureable precipitation, if it occurs at all.

So... in the case of the forecast above, if the forecaster knows precipitation is sure to occur ( confidence is 100% ), he/she is expressing how much of the area will receive measurable rain. ( PoP = "C" x "A" or "1" times ".4" which equals .4 or 40%.)

But, most of the time, the forecaster is expressing a combination of degree of confidence and areal coverage. If the forecaster is only 50% sure that precipitation will occur, and expects that, if it does occur, it will produce measurable rain over about 80 percent of the area, the PoP (chance of rain) is 40%. ( PoP = .5 x .8 which equals .4 or 40%. )

Maybe the forecaster is overestimating his confidence and is figuring 100% confidence for 50% of the area, which while that does figure out to a 50% chance of rain, it may end up raining in only 20% of his area (so a more accurate chance of rain would have been 20%).

Adding the 50% chance in the morning and 50% chance in the afternoon wouldn't give you a total chance for the day.  If you look at an hourly forecast and see three hours of 10%, followed by an hour at 20% and an hour at 50%, that doesn't mean that there's now a 100% chance of rain that day, it means that it's going to get cloudier as the day goes and and the chance in that last hour is still 50%.

To compare it to coin flips, though, you wouldn't be looking for the outcome of individual coin flips.  Each individual coin flip does carry a 50/50, heads or tails probability, but looking for the same outcome two times in a row (heads then heads again) has a probability of 25%, wherease weather forecasting for any given period of time happens more or less independently of any previous period.

 

In any case, I find it best to take weather forecasts as broad generalizations and simply look out a window to make my own determination of whether to bring an umbrella.