Random events often look like nonrandom events.

Extraordinary events can happen without extraordinary causes.

We all create our own view of the world and then employ it to filter and process our perceptions, extracting meaning from the ocean of data that washes over us in daily life.

The human mind is built to identify for each event a definite cause and can therefore have a hard time accepting the influence of unrelated or random factors.

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

Successful people in every field are almost universally members of a certain set—the set of people who don’t give up.

Hollywood studio executive: “If I had said yes to all the projects I turned down, and no to all the other ones I took, it would have worked out about the same.”

The probability that two events will both occur can never be greater than the probability that each will occur individually.

A good story is often less probable than a less satisfactory explanation.

These three laws, simple as they are, form much of the basis of probability theory:

If two possible events, A and B, are independent, then the probability that both A and B will occur is equal to the product of their individual probabilities.

If an event can have a number of different and distinct possible outcomes, A, B, C, and so on, then the probability that either A or B will occur is equal to the sum of the individual probabilities of A and B, and the sum of the probabilities of all the possible outcomes (A, B, C, and so on) is 1 (that is, 100 percent).

When you want to know the chances that two independent events, A and B, will both occur, you multiply; if you want to know the chances that either of two mutually exclusive events, A or B, will occur, you add.

The game has two basic strategies. One is to always guess the color that you notice occurs more frequently. For instance, if green shows up 75 percent of the time and you decide to always guess green, you will be correct 75 percent of the time. The other strategy is to “match” your proportion of green and red guesses to the proportion of green and red you observed in the past. If the greens and reds appear in a pattern and you can figure out the pattern, this strategy enables you to guess right every time. But if the colors appear at random, you would be better off sticking with the first strategy. In the case where green randomly appears 75 percent of the time, the second strategy will lead to the correct guess only about 6 times in 10. Humans usually try to guess the pattern, and in the process we allow ourselves to be outperformed by a rat.

One should not appraise human action on the basis of its results.

The law of small numbers.

Cicero wrote that “probability is the very guide of life.”