The odds of winning the lotto can be a million to one, but if I win it on my first try, then those weren't my odds were they?
From what you quoted it sure looks like after the fact.
Which simply points out the idiocy of trying to apply statistics and science to miracles. All those who suggest such methods are simply being silly.
Miracles by definition are the result of an intentional act and are not, again by definition, repeatable. They are not subject to statistical analysis and any such efforts are simply a waste of time and a sure sign that the person suggesting such tests is pretty clueless about miracles.
If by some miracle someone wins the lotto on their first try, it matters not what the odds were.
I'm really not sure of the reasoning behind the statement. The a priori odds do not change based on the outcome. So the only sensible argument I can see is that if you win first time then the game must be rigged somehow. But even that is wrong. It's not AS wrong - but a single win is very unlikely to be sufficient evidence for such a conclusion.
What I want to discuss is what people think the dangers are to society and individuals in not understanding basic statistics, or even basic math.
As a compulsive gambler, you would think that I was clueless about statistics. I was, but only because I believed in divine intervention on behalf of my statistics. I figured that even if the odds were a million to one, I would be favored somehow and some way.
Pathological gambling is a brain disease that seems to be similar to disorders such as alcoholism and drug addiction. These disorders likely involve problems with the part of the brain associated with behaviors such as eating and sex. This part of the brain is sometimes called the "pleasure center" or dopamine reward pathway.
Treatment for people with pathological gambling begins with the recognition of the problem. Since pathological gambling is often associated with denial, people with the illness often refuse to accept that they are ill or need treatment. Most people with pathological gambling enter treatment under pressure from others, rather than voluntarily accepting the need for treatment.
I am also aware of the gamblers fallacy and can logically understand it. Gambling is not done because one does not comprehend statistics. To cure a compulsive gambler, you don't teach them statistics.
Well Jar says you're being silly, so it's good that you agree.
And he's right - your argument is silly. YOu've given no reason to believe that that person won for any different reason than other people win. Some number comes up, and one of the many people who play happens to have chosen it. It happens all the time.
If you win, the odds are the number of combinations of numbers that result in your winning - 1 - to the number of possible combinations of numbers in total.
You're just being glib, I guess, but you're also being completely inaccurate. Even if you were the only one who played the lottery that time, unless you bought every single number combination, the odds of you winning were not 1 - even if you did win.
This is a thread about understanding statistics. Let's not undercut that aim with glib misrepresentations of mathematics, ok?
After the fact, the odds of you having won are 1 (almost).
The odds don't change after you win.
You still figure the odds by looking at the outcome sample space - the total number of different combinations of lotto numbers - compared to the subset of those outcomes that results in your victory.
In the case of the Powerball, that's 1 in 146 million. Before, after, it doesn't matter. The actual outcome doesn't change the probabilities of any of the outcomes. That something happened or didn't happen doesn't change the probability of it happening.
The odds of getting the number for a particular person cannot be figured, because we don't know what number they will pick, and what number will actually come out.
We know how lotto numbers are generated, so we can develop a sample space of outcomes. We know exactly how many different combinations (not permutations, the lottery doesn't work like that) of numbers are possible.
And it doesn't matter what number any particular individual picks; they all have the same probability of being the winning numbers (because the game isn't fixed.)
There is your objective result, or you data, so now tell us nator, how did that person win?
They won because they picked the winning numbers. Given the average size of the population who buys tickets (and assuming they all play different numbers) we can tell you, on average, how long it will be before somebody wins.
That they picked the winning numbers is not significant. Imagine that you have two machines running - one generates one random lotto number every night, and the other machine generates a hundred thousand random lotto numbers every day. It shouldn't surprise anyone that, every few days or so, there's a match between the number generated by the first machine and one of the numbers generated by the second.
First, I have to point out that your situation is about probability, not statistics, which are different, although they are related and even overlap a bit.
I'm teaching the Introduction to Probability course this term. I've never taken nor taught a probability course before myself (although I have taken and taught statistics courses) so it's been jolly fun.
Taking a cue from the text, the first day I told the class that if I toss a fair coin, the probability that it will land heads is 1/2. Then I asked what did that sentence mean? Some (including myself) would say that it means that if I toss the coin a whole bunch of times, then about half the time the coin should land heads. But what does "about half the time" mean? In fact, it is entirely possible that if I toss a coin 100 times in a row, even if it is fair, I can get heads every time.
I also asked what it would mean if I only intended to toss the coin once. Or what does it mean that the probability of rain tomorrow will be 20%, given that tomorrow will only come once.
So I told them (being an honest sort) that we will develop the mathematical formalism for probability and then learn how to take real situatlions like coin tosses and dealing cards and translate them into the mathematics to calculate the probabilities, and I hoped they wouldn't notice that I never actually answer the original question.