• The law of large numbers states that when an experiment is performed a large number of times, the relative frequency of an event tends to become closer to the true probability of the event; that is, probability is long-run relative frequency.​

• ​The law of large numbers says nothing at all about short-run behavior.

• ​The law of large numbers has two conditions.

• First, the chance event under consideration does not change from trial to trial.

• Second, any conclusion must outcomes is also called the gambler's

  fallacy. be based on a large (a very large!) number of observations.

​

​

​The Law of Large Numbers

​

​There are two games involving flipping a fair coin. In the first game, you win a prize if you can throw between 45% and 55% heads.

​

In the second game, you win if you can throw more than 60% heads.

​

For each game, would you rather flip 20 times or 200 times?

​

​Example 1 Discussion

​

​The probability of throwing heads is 0.5.

By the law of large numbers, the more times you throw the coin, the more the relative frequency tends to become closer to this probability. With fewer tosses, there is greater chance of wide swings in the relative frequency. Thus, , you would rather have 200 flips in the first game, whereas in the second game, you would rather have only 20 flips.

​

​Example 1 Discussion

​

​Basic Probability Rules

​Basic Probability Rules

​Basic Probability Rules

​What is the probability that someone in this group uses the "guess" strat

​Basic Probability Rules

​What is the probability that someone in this group uses the "guess" strat