![]() (They are more structured than the others.) They are also the least likely, only 2 out of 32 possibilities. The two most orderly possibilities are 5 heads or 5 tails. With any system, the assumption that all microstates are equally probable must be valid, or the analysis will be erroneous. With coin tosses, this requires that the coins not be asymmetric in a way that favors one side over the other, as with loaded dice. Note that all of these conclusions are based on the crucial assumption that each microstate is equally probable. Similarly, it is equally probable to get 5 tails as it is to get 5 heads. Not surprisingly, it is equally probable to have the reverse, 2 heads and 3 tails. The macrostate of 3 heads and 2 tails can be achieved in 10 ways and is thus 10 times more probable than the one having 5 heads. On the large scale, we are concerned only with the total heads and tails and not with the order in which heads and tails appear. What are the possible outcomes of tossing 5 coins? Each coin can land either heads or tails. To illustrate this fact, we will examine some random processes, starting with coin tosses. It is not impossible for rain to fall in an orderly pattern, just highly unlikely, because there are many more disorderly ways than orderly ones. Some fall close together, some far apart, but they never fall in straight, orderly rows. When you watch an emerging rain storm begin to wet the ground, you will notice that the drops fall in a disorganized manner both in time and in space. Disorder is simply vastly more likely than order. Why should heat transfer occur only from hot to cold? Why should energy become ever less available to do work? Why should the universe become increasingly disorderly? The answer is that it is a matter of overwhelming probability. The various ways of formulating the second law of thermodynamics tell what happens rather than why it happens. Why doesn’t heads come up 100, 90, or even 80% of the time? (credit: Jon Sullivan, ) Figure 15.37 When you toss a coin a large number of times, heads and tails tend to come up in roughly equal numbers.
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