Quotes About Probability

The belief otherwise is sometimes called "the gambler's fallacy." In fact, if you flip a fair coin 1,000,000 times and get 1,000,000 heads in a row, the probability of getting tails on the next flip is still ½. The

Os maiores riscos nunca são aqueles que você pode ver e mensurar, mas aqueles que você não pode ver e, portanto, jamais poderá mensurar. Aqueles que parecem tão distantes, fora das fronteiras da probabilidade normal, que você não consegue nem imaginar que possam acontecer na sua vida – mesmo que, é claro, aconteçam, com mais frequência do que você se dá conta.

Yes, the probability that five people in the same school or church or workplace will contract the same rare form of leukemia may be one in a million, but there are millions of schools and churches and workplaces

Probability tells us that any outlier—an observation that is particularly far from the mean in one direction or the other—is likely to be followed by outcomes that are more consistent with the long-term average.

The central limit theorem tells us that in repeated samples, the difference between the two means will be distributed roughly as a normal distribution.

But probability triumphs in the end. An important theorem known as the law of large numbers tells us that as the number of independent trials increases, the average of the outcomes will get closer and closer to its expected value.

I won $2 playing the lotto today. And I might win $2 again tomorrow. But if I buy thousands of $1 lottery tickets, each with an expected payout of $.56, then it becomes a near mathematical certainty that I will lose money.

The law of large numbers explains why casinos always make money in the long run.

The decision tree lets you know that your expected payoff is far higher than what you are being asked to invest.

On the other hand, the most likely outcome, meaning the one that will happen most often, is that the company will not discover a cure for baldness and you will get only $250,000 back.

The law of large numbers suggests that an investment firm, or a rich individual like Warren Buffet, should seek out hundreds of opportunities like this with uncertain outcomes but attractive expected returns. Some will work; many won't. On average, these investors will make a lot of money, just like an insurance company or a casino.

The larger the number of samples, the more closely the distribution will approximate the normal distribution.

If there are 60,000 blue marbles and 40,000 red marbles in a giant urn, then the most likely composition of a sample of 100 marbles drawn randomly from the urn would be 60 blue marbles and 40 red marbles.

some might have 62 blue marbles and 38 red marbles, or 58 blue and 42 red. But the chances of drawing any random sample that deviates hugely from the composition of marbles in the urn are very, very low.

The t-distribution is actually a series, or "family," of probability density functions that vary according to the size of our sample.

A statistical anomaly does not prove wrongdoing. Delma Kinney, a fifty-year-old Atlanta man, won $1 million in an instant lottery in 2008 and then another $1 million in an instant game in 2011. The probability of that happening to the same person is somewhere in the range of 1 in 25 trillion.

Statistics cannot prove anything with certainty. Instead, the power of statistical inference derives from observing some pattern or outcome and then using probability to determine the most likely explanation for that outcome.

Second, even if the underlying data could accurately predict future risk, the 99 percent assurance offered by the VaR model was dangerously useless, because it's the 1 percent that is going to really mess you up.

In some ways, the VaR debacle is the opposite of the Schlitz example in Chapter 5. Schlitz was operating with a known probability distribution

Bottles of wine cannot be magically rearranged to suit the results of a search. They cannot be popped onto the next shelf to optimize the probability that people like you who bought aged Gouda and black olives might also like this Pinot. Atoms are stubborn this way.

Permaina adalah uraian matrmatis dari hubungan antara strategi-strategi dan kemungkinan hasil-hasilnya.

No. It will eventually manifest itself again, but it won't be the same personality as before; though at the same time it won't be a different personality either. 'Same' and 'different' are far too specific. And it won't have learned what I want to know. It will simply happen to know it this time. Or, if not this time, it will know it some time. It's like waiting for two or twelve to come up in a game of dice.

Chance is a funny thing. A fat one and a slim one are the same thing.

That's damned likely," Gant interjected