We have a new camera over Lake of Ozarks…a beauty of a shot!
Like it? This morning I showed it as a boat was cruising along and a thunderstorm rain shaft was approaching from the distance. In this shot you can see some shafts of rain in the distance
T-storms were firing strong in the vicinity of KC this morning. Sedalia reported some small hail…there was a lot of lightning with a band of t-storms approach from the west. They weakened dramatically while approaching KC resulting in weak scattered showers. These showers pass and we dry up afternoon and warm to the low-mid 60s.
This was our weekend weather trivia from today. Can you pull your statistics from memory and figure this one out?
Yeah, you can draw a Venn Diagram, but I thought the easiest way to show the answer on air was with this graphic:
Since each day is a 50/50 shot, the possibility that we’d have rain at some point this weekend encompasses the top three out of four equally likely possibilities. I should have drawn a table, right. The point is you can’t add 50% to 50% and get a 100% chance for rain. Fun?
And I just received an email from a local Meteorologist who will remain nameless about this subject:
Just caught your trivia segment about rain chances and probabilities. Unfortunately, the correct answer to your question was not listed. It is *not* 75%.
If there’s a 50% chance of rain Saturday and a 50% chance of rain Sunday, the chance of rain over the weekend is still 50%. Each day’s forecast is an independent occurrence.
Let’s equate this to a coin flip. Let’s say that “heads” = rain and “tails” = no rain. An identical 50/50 proposition.
No matter how many times you flip a coin, there is still a 50% that you get heads on any individual flip. If there was a 75% chance that you would get heads on one or both of the two flips, casinos would not exist and I would be raking in billions at the Baccarrat or Roulette tables.
The confusion lies in the difference between unique event probability and possible outcomes. Yes, on two coin flips there are 4 possible outcomes of those two flips, 3 of which are favorable to heads (rain). However, the expectation at getting one of those possible outcomes not equal.
As an FYI, my mom has taught college statistics since before I was born, and so this sort of thing is second nature to me. I’m hoping that you will correct this graphic as this places an incorrect understanding of how weather forecasts work in the eye of the general public.
I replied with the following email:
The coin flip was the exact analogy I used to explain this to my coworkers
With the coin flip analogy, the question becomes “What are my chances to flip heads at least once if I am given two flips of the coin?”
This is not an “individual flip”…it’s two separate, independent flips.
The answer is 75% and can be proved by constructing a simple Venn Diagram.
Why two coin flips? Because they represent two SEPARATE storms, each with a 50% chance to rain on a SEPARATE days. The probability of each dropping rain doesn’t change…but that wasn’t the question…the question (was) can rain fall AT LEAST ONCE given these two independent “flips”.
As for your casino analogy, winning ONE TIME on the roulette wheel is more likely with a group of 38 spins as opposed to an individual spin. However, the winning probability of each spin remains the same as it is independent of other spins. Unfortunately, each time you spin, you must pay. The house will always have the same advantage, remaining unchanged for each spin.
We can talk about this more…call me at the station today after 2pm.
Ask for weather
I just received this reply from the same person:
What do you think?