Math for the chance of rain
The chances it's not going to rain in each of those hours is the inverse (30%, 60%, 70%, 60%), and the chances that it won't rain in *any* of those times is 30% x 60% x 70% x 60% = 7.6%. Therefore, the chances that will rain at some point is 92.4%.
However, the forecast also says that the chance of rain today is 60%.
What gives?
Then again, if the chance of rain at 2 PM is 70%, then the chance of any rain at all must also be at least 70%.
I'm so used to gambling being independent events, I forget that the rest of the world doesn't always work that way.
Good point about the 70% quirk. That should have occurred to me.
If there is a 1/60 chance it rains during any minute of the next 24 hours, then the chance of getting rain in exactly 24 minutes of those 24 hours is approximately:
1 / (2π * 59/60 * 24)^.5 =~ 8.2%
Showoff.Quote: Ace2If there is a 1/60 chance it rains during any minute of the next 24 hours, then the chance of getting rain in exactly 24 minutes of those 24 hours is approximately:
1 / (2π * 59/60 * 24)^.5 =~ 8.2%
Quote: MichaelBluejaySeems like the chance of rain is always 50-50. It’s either gonna rain or it’s not.
Not if you're in Seattle. Then it's either: sunny, a light drizzle, rain, or a torrential downpour; so about 75%.
Consider an 8x10 grid. What is the least number of marks needed to put on the board so that three 2x2 squares can't be placed on it without overlapping a mark?
I just did a Google search and found these articles on the topic.Quote: GM70% chance of rain at 2 pm means that the meteorologist thinks that there is a 70% chance that there will a measurable amount of rain between 1 pm and 2 pm somewhere in the relevant area. It does not mean the probability of it raining at 2pm. There must be a different type of definition for the probability of rain during a day, because my local forecast says 65% chance of rain on Tuesday, but 75% chance of rain at 7 am.
https://www.wmcactionnews5.com/2019/04/25/breakdown-what-does-rain-percentage-really-mean-you/
https://www.thv11.com/article/weather/what-does-percent-chance-of-rain-mean/91-f59f5e4e-5cca-4a44-8ec6-72397387969d
I had a conversation maybe 20 years ago with the TV meteorologist on our local ABC affiliate station. The TV meteorologist said that when he used these terms in his forecast, he often thought of them in descriptive terms. For example, 10% was used for light rain, 30% indicated spotty showers, 70% was steady light to medium rain. And so on. At the time he insisted that 10% meant it would rain over 10% of the area with 100% probability. I complained to the TV station that he was absolutely incorrect in his interpretation. He apparently did his research after my complaint as he changed his forecast language shortly after.
Quote: MichaelBluejayThe weather forecast says that for the rest of the day, there's a 70%, 40%, 30% and 40% chance of rain at 2, 3, 7, and 9pm, respectively.
The chances it's not going to rain in each of those hours is the inverse (30%, 60%, 70%, 60%), and the chances that it won't rain in *any* of those times is 30% x 60% x 70% x 60% = 7.6%. Therefore, the chances that will rain at some point is 92.4%.
However, the forecast also says that the chance of rain today is 60%.
What gives?
Come on Michael! CORRELATED
Edit…. which was mentioned upthread before I posted my response….
I will golf if the number during any hour I’ll be playing doesn’t exceed 30%. Last few times we had 20% and 30% hours we had zero rain.
Quote: MichaelBluejayIt's always seemed to me that the meteorologists are fudging. It's either gonna rain or it's not, so in that sense there's no *chance* of rain, and when a meteorologist says there's an 80% chance of rain, what s/he's actually referring to is his/her *certainty* about whether it's gonna rain. It seems like meteorologists defend their limited understanding by blaming nature as being unpredictable. Well, nature isn't unpredictable like dice rolls: dice rolls can't be predicted because they're truly random, weather can't be predicted with better accuracy not because it's truly random, but because our human-based models are imprecise.
Dice rolls can be predicted in principle, you just need to know the initial conditions very accurately. The weather is chaotic in the technical sense of the word, which makes accurate long term forecasts impossible.
Quote: WizardThe following question was asked in a comment in my video on Da Vinci Diamonds keno.
Consider an 8x10 grid. What is the least number of marks needed to put on the board so that three 2x2 squares can't be placed on it without overlapping a mark?
Did you mean to put this here, or in the Easy Math Puzzles thread?
The best answer I have found is 19 - the 0s are the marks:
# # # # # # # # # #
# 0 # 0 # 0 # 0 # #
# # # # # # # # # 0
# 0 # 0 # 0 # 0 # #
# # # # # # # # # #
# 0 # 0 # 0 # 0 # 0
# # # # # # # # # #
# 0 # 0 # 0 # 0 # 0
Quote: GMDice rolls can be predicted in principle, you just need to know the initial conditions very accurately. The weather is chaotic in the technical sense of the word, which makes accurate long term forecasts impossible.
Absolutely agreed. Quantum mechanics is truly random (we think). Everything else is just human uncertainty of outcome.
Quote: MichaelBluejayIt's always seemed to me that the meteorologists are fudging. It's either gonna rain or it's not, so in that sense there's no *chance* of rain, and when a meteorologist says there's an 80% chance of rain, what s/he's actually referring to is his/her *certainty* about whether it's gonna rain. It seems like meteorologists defend their limited understanding by blaming nature as being unpredictable. Well, nature isn't unpredictable like dice rolls: dice rolls can't be predicted because they're truly random, weather can't be predicted with better accuracy not because it's truly random, but because our human-based models are imprecise.
The other part of this is that storms are often scattered.
Ever see it rain across the street but not where you are standing?
I think people often have unrealistic expectations a forecast for a city to apply to whatever city block size area they are in.
Quote: ThatDonGuy
Did you mean to put this here, or in the Easy Math Puzzles thread?
The best answer I have found is 19 - the 0s are the marks:
# # # # # # # # # #
# 0 # 0 # 0 # 0 # #
# # # # # # # # # 0
# 0 # 0 # 0 # 0 # #
# # # # # # # # # #
# 0 # 0 # 0 # 0 # 0
# # # # # # # # # #
# 0 # 0 # 0 # 0 # 0
Yes, I did mean to post my puzzle here.
19 beats the best I could think of.
Quote: WizardYes, I did mean to post my puzzle here.
19 beats the best I could think of.
Question: can the three 2x2 blocks overlap?
If not, then my solution can be reduced to 18 by removing the mark in the lower right corner and moving the remaining one farthest down in the right column by one row.
I also tried a random search, leaving the top row and left column empty (I randomly ordered the remaining 63 squares and added marks in that order until there were fewer than three 2x2 empty squares, including overlaps), but after around 250 million attempts, the best I got was 20.
We all game a him a quizzical look. Weatherman is your dream job? He responded saying, "In what other occupation can you be wrong 50% of the time and still keep your job?!"
