Question

The Law of Large Numbers is a statistical theory that you read about in this chapter. In your own words, what does this law say about the probability of an event? Perhaps you have also heard of something called the Law of Averages (also called the Gambler's Fallacy). Do an Internet search to find out additional information about both of these laws.

Are these the same laws? If not, how are they related and how are they different?

What general misconceptions do people have regarding these ideas?

Consider the following scenarios, commenting on the validity of the reasoning that is being used. After an unusually dry autumn, a radio announcer is heard to say, "Watch out! We'll pay for these sunny days later on this winter." A batter who had failed to get a hit in seven consecutive times at bat then hits a game-winning home run. When talking to reporters afterward, he says he was very confident that last time at bat because he knew he was "due for a hit."

Commercial airplanes have an excellent safety record. However, in the weeks following a crash, airlines often report a drop in the number if passengers, probably because people are afraid to risk flying. A travel agent suggests that, since the law of averages makes it highly unlikely to have two plane crashes within a few weeks of each other, flying soon after a crash is the safest time. In a Monte Carlo casino in 1913, the color black came up a record twenty-six times in succession in roulette. There was a near-panicky rush to bet on red, beginning about the time that black came up the fifteenth time. Why?

Please share the URLs of any Internet resources that you utilize as you discuss this topic with your peers.

Answer 1

After an unusually dry autumn, a radio announcer is heard to say, "Watch out! We'll pay for these sunny days later on this winter."

the radio announcer is reffering to the "law of averages" assuming the events are independent, the weather is not more likely to be bad in the winter because of a few sunny days in autumn.

A travel agent suggests that, since the law of averages makes it highly unlikely to have two plane crashes within a few weeks of each other, flying soon after a crash is the safest time

the probability of there being a crash will always be the same regardless of whether or not there was a crash two weeks before or a minute before. A crash has no affect on the probability of a crash happening. So, the travel agent is incorrect, because the law of averages says that an event will occur because it is "due to happen", but this is incorrect the probability of an event happening is always the same unless something happens that makes airplane flying safer.

In a Monte Carlo casino in 1913, the color black came up a record twenty-six times in succession in roulette. There was a near-panicky rush to bet on red, beginning about the time that black came up the fifteenth time.

This was not a wise decision, because it does not makese sense that RED and BLACK will appear equal times. Although they have equal probabilty, but Based on the previous records there is more chance of coming black than red, so he should go with black.