What is probability?
What does it mean to say one event is more likely than another? Looking back in time everything that has happened seems fixed, looking forward anything is possible. If you throw a dice you don’t know which number will be uppermost, you throw the dice and get a six. What happens to the other five possibilities? At what instant does the possibility become a certainty? What changes?
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Probably got sonething to do with chance.
Probability is the reason why I’d never win the lottery, and why I don’t waste any money buying tickets.
Democrats in the White House: 1933–1952
Republicans in the White House: 1953–1960 8 Years
Democrats in the White House: 1961–1968 8 Years
Republicans in the White House: 1969–1976 8 Years
Democrats in the White House: 1977–1980 4 Years
Republicans in the White House: 1981–1992 12 Years
Democrats in the White House: 1993–2000 8 Years
Republicans in the White House: 2001–2008 8 Years
Democrats in the White House: 2009— ? 8 Years plus…
Anything can happen, but the probability is that in 2017 the Republicans are in the White House again.
Pretending to kind of know the outcome.
@flutherother Really? It’s Derren Brown. Well, maybe that’s why.
Basically, what he does is flip a coin 10 times in a row and gets heads. To understand how he did that is to understand probability.
The following is called the frequentist interpretation of probability, which is the standard definition:
If an event E has a probability of P% of occurring in each trial, then around P% of trials will result in the event E occurring, in the long run.
If the probability of a coin landing on heads is 50%, then around 50% of all coin flips will result in heads.
If you toss a coin only once, the result will be either 0% heads or 100% heads. As you toss the coin multiple times, however, the result converses closer to 50%. Eventually, if you toss the coin 1000000000 times, then the percentage of heads in that sample will be very close to 50%.
Probability is the chance that a certain event/outcome will happen. For instance, if you roll 2 six-sided dice, there is a 1-in-36 chance of getting double-sixes.
@Rarebear @filmfann There are ways to affect probability. Carnies do it all the time with coin-tosses, making a 50/50 toss come up their way >90% of the time, and the Republicans have damaged their chances for 2016 badly enough that we probably won’t see a Republican in the Oval Office until at least 2020. (No, I’m not turning this into a politcal thread; read on….)
Now, @Rarebear also demonstrates something about probability called The Monte Carlo Fallacy. Contrary to popular belief, past results don’t have any bearing on future ones. Suppose, for instance, that you toss a coin fairly such that it’s a 50/50 shot (no carnie tricks!) and it comes up heads 47 times in a row. The Monte Carlo fallacy says that it’s sure to come up Tails on the 48th flip when the truth is that the other 47 flips don’t affect that fact that the toss is still a 50/50 chance.
@jerv So did you figure out how he got 10 heads (fairly) in a row?
@Rarebear I watched the rotation. The 4th flip was a giveaway, but suffice it to say that if you start in the same orientation and gauge the rate of rotation correctly, chance is removed. Of course, putting it at a slight angle with a around the Z-axis spin can make the wobble look like a normal X/Y-axis rotation as well.
Or you can just cheat and film a series of flips until you hit the 1-in-1024 (or 2^10) series of 10 consecutive heads. 1-in-1024 isn’t terribly unlikely.
@jerv What he did was film for 9 hours, and he flipped the coin about half a million times. They took the clip where it happened to have 10 heads in a row.
I came across this probability paradox:
A factory produces cubes with side-length between 0 and 1 foot; what is the probability that a randomly chosen cube has side-length between 0 and ½ a foot?
A factory produces cubes with face-area between 0 and 1 square-feet; what is the probability that a randomly chosen cube has face-area between 0 and ¼ square-feet?
A factory produces cubes with volume between 0 and 1 cubic feet; what is the probability that a randomly chosen cube has volume between 0 and 1/8 cubic-feet?
Three different ways of stating the same problem but each gives a different answer, 50%, 25% and 12.5%.
@flutherother, the answer only changes based on the assumptions one makes. You never describe the distribution of different sizes. The first wording leads you to believe they’re distributed evenly over the different possible side-lengths, the second over face areas, the third over volumes. That’s what leads to these alternate answers. They’re not all three the same problem, unless you give more information on their distribution, and if they’re distributed the same, then we’ll get the same probability for each.
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