Dice don't remember!
Statistical significant: You need a certain number of occurrences before there is the possibility of a relation between events.
Even if there is a statistical significance, it is not a proof. It just allows you to now try to find the reasons for the relation.
Just to keep you grounded:
- Statistical significance is NOT like PI. It is just a chosen value. And sometimes you have to think for yourself and ignore it. There are tests where people were shown data and told about the statistical significance of something in the data. If the people had knowledge about statistics, only 15% gave correct answers. If people without knowledge about statistics and "statistical significance" where asked, 75% gave the correct answers.
- If you find a "statistical significance" between sold chocolates and stolen radios, would you think there is a relation? Why? Why not?
- If you find a "statistical significance" between sold alcohol and abuse, would you think there is a relation? Why? Why not?
- Blinded by Statistical Significance
- A bad definition of statistical significance from the U.S. Department of Health and Human Services, Effective Health Care Program
Physical objects we use for statistics
Whenever we talk about physical objects here, we mean perfect physical objects. A dice is a perfect dice with the exact same chance for each side. A coin is perfect, with exactly 50% chance for each side, there will be no corner cases like a coin standing or such things. If the coin is standing I'll shoot you, so you will never know. The coin is perfect!
Multiple times the same choice
If you throw a coin then you have 50% chance for each side each time. If you throw a coin two times there are four cases:
- heads / heads
- heads / tails
- tails / tails
- tails / heads
Nothing special here. Because the chances for each event are the same it is very easy. Each of the four cases has a 1/4 (25%) chance of happening.
What you have to keep in mind is that "Dice don't remember!". And coins don't remember too. So if you had 99 times "heads", the chance for the 100th throw to be heads is still 50%.
Different chances in a row
So what do you do if you want to know the chance for a certain event when you mix different events? You multiply the chances which you see as value between 0 and 1.
Multiply the chances
Chance for coin/head/chance(100/2)% followed by dice/1/chance(100/6)%?
50% => 0.5 (100/6)% = 16.67 => 0.17 0.5 x 0.17 = 0.085
So see it as percent from 100 multiply with 100 again:
0.085 * 100 = 8.5
So for a coin/head followed by a dice/1 the chances are 8.5%.
Just think, how many paths are there?
Now, there is another way too. How may possible paths are there when you first throw a coin and then throw a dice, how many paths are there? Of course
2 * 6 = 12
So we 12 possible paths. The chance for each path is the same, so the chance is
100 / 12 = 8.3
This is not the same?
First we got 8.5, now we got 8.3, one of them is wrong!111!!!!11 (no, not really)
Yeah, yeah. This is math. The problem is in the "100/6 = 16.67 => 0.17" above.
If you'd keep 0.1667 then you'd get 0.08335 instead of 0.085 and if you'd use
16,66666666666667 * 0.5 you'd get 8,333333333333333
So... depending on how many digits you keep and how exact you are when calculating you get different results.
But it is not really relevant, because it will make no difference if you think the chances are 8.3% or 8.5%. Or would you come to a different conclusion because of the 0.2% difference?
Monty Hall problem
The "Monty Hall problem" shows how pseudo science can influence people. Currently - 2023-08-29 - there is an entry in the Wikipedia which uses over 50000 (yes, that are 50 thousand) letters to tell us that the chance of a win between two equal choices is 1/3 instead of 1/2.
You find a lot of articles who tell you the same. You find books and web novels where the protagonist is the only one smart enough to understand that the solution is 1/3.
The problem is, this is wrong.
Remember the first rule? "Dice don't remember!" Gates don't remember too.
So, it is of NO relevance how many doors there were before or what the moderator thinks or says.
You have a situation with two equal chances which makes the chance for a win 50% and the chance for a loss 50%.
Why? Because gates don't remember!
All that smart ass talk which goes around and around and seems so incredible smart, it is just wrong and common sense gives the right answer.