Quotes About Probability

Over the hundreds of at bats he has each year, those random factors usually average out and result in some typical home run production that increases as the player becomes more skillful and then eventually decreases owing to the same process

Random events often look like nonrandom events, and in interpreting human affairs we must take care not to confuse the two.

Just as, looking at a Rorschach blot, you might see Madonna and I, a duck-billed platypus, the data we encounter in business, law, medicine, sports, the media, or your child's third-grade report card can be read in many ways. Yet interpreting the role of chance in an event is not like intepreting a Rorschach blot; there are right ways and wrong ways to do it.

The Drunkard's walk: how randomness rules our lives / Leonard Mlodinow.

the same mathematics that describes drawing pebbles from an urn can be employed to describe any series of trials in which each trial has two possible outcomes, as long as those outcomes are random and the trials are independent of each other.

regression toward the mean. That is, in any series of random events an extraordinary event is most likely to be followed, due purely to chance, by a more ordinary one.

in real-life situations we often make the opposite error: we assume that a sample or a series of trials is representative of the underlying situation when it is actually far too small to be reliable.

The idea that the odds of an event with a fixed probability increase or decrease depending on recent occurrences of the event is called the gambler's fallacy.

Jakob Bernoulli had shown that through mathematical analysis one could learn how the inner hidden probabilities that underlie natural systems are reflected in the data those systems produce.

We cannot know whether our single observation represents the mean or an outlier, an event to bet on or a rare happening that is not likely to be reproduced.

According to the laws of chance, if you look around enough, you are bound to find something interesting.

that in a random series of 101,000,007 zeroes and ones, you should expect at least 10 nonoverlapping subsequences of 1 million consecutive zeros.11

A FEW YEARS AGO a man won the Spanish national lottery with a ticket that ended in the number 48. Proud of his "accomplishment," he revealed the theory that brought him the riches. "I dreamed of the number 7 for seven straight nights," he said, "and 7 times 7 is 48.

if events are random, we are not in control, and if we are in control of events, they are not random. There is therefore a fundamental clash between our need to feel we are in control and our ability to recognize randomness. That clash is one of the principal reasons we misinterpret random events.

We miss the effects of randomness in life because when we assess the world, we tend to see what we expect to see. We in effect define degree of talent by degree of success and then reinforce our feelings of causality by noting the correlation.

So the relevant question is, if thousands of people are tossing coins once a year and have been doing so for decades, what are the chances that one of them, for some fifteen-year period, will toss all heads?

law of large numbers is employed because, as we've said, Bernoulli's theorem concerns the way results reflect underlying probabilities when we make a large number of observations.

Pearson invented a method, called the chi-square test, by which you can determine whether a set of data actually conforms to the distribution you believe it conforms to.

there remains the big picture, the question of how much randomness contributes to where we are in life and how well we can predict where we are

Statistically, the probability of any one of us being here is so small that you'd think the mere fact of existing would keep us all in a contented dazzlement of surprise.

Statistically, the probability of any one of us being here is so small that the mere fact of our existence should keep us all in a state of contented dazzlement.

You, dear reader, have now two accounts to choose between and there can be no doubt which is most probable.

I, in any case, am convinced He does not play dice with the universe.

Jedenfalls bin ich überzeugt, dass der [Herrgott] nicht würfelt.