Replies • 16

If you didn't know the answer yourself? How is this a pop quiz?

Alot of people already went over the PoP, precipitation and what the weatherman is telling you when he says 50%

But are you aware that on April 1st 1990, at the SKydome in Toronto, Ontario, Canada with an attendance of 67,678 People, The Ultimate Warrior in a chilling upset defeated Hulk Hogan and became the first Wolrd Heavyweight Champion and Interconterntial Heavyweight Champion.


You multiply the probabilities and invert the result. In this case, a 50% chance of not raining in the morning times a 50% chance of not raining in the afternoon equals a 25% of not raining all day. This leaves a 75% chance of rain for the day.

The coin flip analogy would be the probability of heads happening at least once in two flips.


Tcharr said:

You multiply the probabilities and invert the result. In this case, a 50% chance of not raining in the morning times a 50% chance of not raining in the afternoon equals a 25% of not raining all day. This leaves a 75% chance of rain for the day.

The coin flip analogy would be the probability of heads happening at least once in two flips.

Ding.Ding. There are several ways to answer this quetion.


(1) 'Sherlock' method: by exluding all wrong answers.

  • "Impossible to tell" - Is obviosly wrong. Impossible questions exist aplenty, but they typically aren't verifiable, falsifiable or testable.
  • "100%" -Two uncertainties can hardly add up to 100% chance.
  •  "0% - 50%" Probablilites have to be within a range of 0 to 1. You can add an infinite number of probabilites by making infinitessimal steps. However adding a  non-zero-chance, has to increase the result, chance of rain can neither decrease nor remain the same.
  • "66% + 99%" nobody picked these, but they are intuitive answers (estimates) and closest to the right answer. No simple arithmetic can produce these out of the numbers given: 2 events ; 2 outcomes; 1/2 chance.
  • "75%" Has to be the right answer, because we have excluded all wrong answers.

(2) The intuitive method of adding probabilites (not taught in schools because it's recursive).
We start with a probability of 0.5. The added term has to be adjusted by multiplying it with the remaining probablity.
(chance of rain morning) + (chance of rain afternoon * remaining probability (dry) morning) = combined chance
0.5 + 0.5 * (1-0.5) = 0.75
Example 2: Three upcomming spins of Russian roulette. Chance of shot.
1/6 + 1/6 * (5/6) + 1/6 * (1 - sum of all previous terms) = 91/216 (42%)

(3) School method / (Conditional Probability tree) Map all outcomes as a branching tree. Along the branch probabilities are multiplied, while all branches should add up to 100%.
Possible outcomes
                        ╔ rainy afternoon (0.25) [v]
Rainy morning ╣
                        ╚ dry afternoon   (0.25) [v]
                     ╔ rainy afternoon (0.25)  [v]
Dry morning  ╣

                     ╚ dry afternoon     (0.25) [-]    

(4) Clever school method.
Instead of calculating chance of rain, figure out the chance that it it remains dry. 0.5 * 0.5 = 0.25. The chance of rain therefore is 1-(0.25) = 0.75

edited

no there is no way to answer this question because reguardless of our technology weather is unpreditctable 


Chromigula said:

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%. )

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%, [...]

To compare it to coinflips the number of outcomes increases as their chance drops to 25%.  Heads or Tails (H or T) becomes ( HH or HT or TH or TT).

Thanks for looking up the PoP definition. It is curious how they apply a probability to an area. But it doesn't change anything mathematically. Now that I have opportunity to procrastinate, I thought about it and basically A (area%) is just another probability. It goes from 0 to 100%. Whereas C (confidence) is more or less = 1 in the actual weather simulation, which by the way are extremely accurate and reliable about 3 days ahead.

Rain isn't usually a random event, cloud density and low air pressure means very high certainty of rain. However selecting a time and place where it rains is like a random experiment. If a thick cloud covers half of an area, but you don't know which half will get wet, then it is exactly the same as if thin clouds (50% confidence) covered the entire area.

50% PoP means you are going to get wet an average 50 out of a 100 times with this same forecast, even though your umbrella just occupies one square meter or 9 sq. ft. 

Combining predictions for large areas doesn't make much sense, it always rains somewhere. However combining time intervals makes sense for as long as you have to plan ahead.

  • 3 hours of 10%, 1 hour of 20% and 1 hour of 50% would "add" up to a (1-0.9³ * 0.8 * 0.5)  = ~71% PoP for 6 hours ahead.

 


2 chances. Morning and afternoon. Its basically flipping a coin and asking if one of the 2 chances is heads. 

You could divide the day into 24 hours.

Flip a coin 24 times, I'd gamble everything that I have that heads (50% chance each time) would come up at least once.

But weather forecast is not multiple chances. Its a single chance that can increase or decrease probability depending on the time of day you do the flip.