【文章內(nèi)容簡介】 case, Murphy39。s Law of Falling Toast says: Toast which falls from a table will land butteredside down. Actually, the probability of this happening is extremely high. It39。s close to 100 percent. Now, here39。s why. When something like a piece of toast falls from a table, its behavior is not random. The rate of spin is controlled by the laws of physics. This is the problem. The rate of spin, that is, how fast the toast spins, is too low for the toast to make a plete revolution. It39。s too slow to turn pletely around and hit the floor butteredside up. The rate of spin is determined by the force of gravity. So in a very real sense, the laws of physics, and specifically the rate of spin, make sure that our toast lands butteredside down almost all the time. So the point is that simple probabilities—for example, the probability that toast has a fiftyfifty chance of landing butteredside up—can be greatly affected by other more fundamental factors, such as the laws of physics. So, in this case, we believe that we have bad luck because we don39。t understand that the natural laws of physics are in effect. The toast should land butteredside down. OK? Let39。s look at the next point.Now we e to one of my most frustrating situations in life—the supermarket line. In this case, Murphy39。s Law of Supermarket Lines says: The line next to you will move faster than yours. Now everybody wants to get into the fastest line when they go to the supermarket, right? OK, so let39。s say that you39。re at your local supermarket and there are five lines, but each of the five lines looks pretty much equal in length. Now, of course, you want to try to anticipate which one of the five lines will move the fastest. Well, this is where simple probability theory enters the picture. The chances that you have chosen the fastest of the five lines is one divided by the number of lines, which is five in this case. So mathematically, the formula is one divided by N where N is the total number of lines. So in this example, one divided by five gives us what?STUDENT 2: One divided by five is onefifth or . . . uh . . . 20 percent.TEACHER: Right. Twenty percent. There39。s only a 20 percent chance that we have chosen the fastest of the five lines. Now even if we reduce that to three lines, our line and the lines on each side of us, the chances we39。ve chosen the fastest line are still only what?Student 2: Uh, 33 percent. One out of three.TEACHER: Sure. One divided by three is 33 percent, so it39。s not just your imagination that one line near you almost always moves faster than yours. Simple probability theory shows that the odds are against you. If there are very many lines, the chances that you39。ll choose the fastest one is quite low. So, you see, it has little to do with luck, but we perceive that it does.All right. Now let39。s look at a final situation that shows how we monly misunderstand the laws of probability. We39。ve e to Murphy39。s Law of Gambling that says simply: You will lose. Now in the case of the supermarket lines that we39。ve just talked about, probability theory applied very nicely. And actually, as we go through life, most things are fairly predictable because they follow the basic laws of probability. Weather is an example. Let39。s say that it39。s been raining for a week, and a friend says to you I think it39。s going to be sunny tomorrow. Is that an unreasonable statement? Well, no. Clouds move, and they are of limited size, so if it39。s been raining for a week, it39。s likely that the rain and clouds will end soon. In other words, the next sunny day is more likely to occur after the seventh day of rain than after the first, because the storm front has what is called a life history. Now this is important, so let me explain that term. Events with a life history have changing probabilities of certain events occurring over time. For instance, uh, if you plant flower seeds, you can predict with reasonable accuracy when the plants will e up, when they will bloom, and how long they will bloom. For instance, with some types of flowers, there39。s a 90 percent chance that they will e up fifteen to twenty days after the seeds have been planted. In short, the growth of a flower follows a clear predictable pattern, and we call this pattern a life history. But this is the trick with many gambling games. The casino owners want us to believe that dice also have a life history and that we can therefore estimate the probability of events related to the dice. However, gambling devices like dice are different because they don39。t have life histories. Now . . . what do you think that means?STUDENT 1: There aren39。t any reliable patterns? Um, just because I rolled a seven last time doesn39。t tell me anything about the next roll.TEACHER: Right. You can39。t look at the past rolls of the dice and predict what the next roll will be. Now many people, especially gamblers, think that they can, but this is what39。s called the gambler39。s fallacy. The gambler39。s fallacy is expecting to roll a seven with a pair of dice because a seven hasn39。t e up recently. So, in other words, there39。s a widespread belief among gamblers that dice have a life history. In thereal world, that39。s not a bad way to reason, but in a casino, it39。s the path to financial loss. Dice have no memory, no life history. Now you can predict that if you roll one dice many, many times, the number five will e up about 16 percent of the time. That39。s one divided by six. But that39。s not what we39。re concerned with here. We39。re concerned with the next roll of the dice. As a result, the element of arbitrariness or randomness makes prediction of the next roll impossible. Statisticians who work with probability theory call the roll of a pair of dice a singleevent probability, and many of these same statisticians believe that the probability of a single event can39。t even be puted mathematically. So, the same probability theory that works well with supermarket lines won39。t help you win a millio