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Two heads in two flips

The problem is: You know that, on the average a nickel will come down on its "head" side once in two tries. That is, the "CHANCE" (note the word) of a nickel coming down heads is 50% or 0.50. Now -- what is the chance that the nickel will come down heads twice in a row? How could we find out? Stop now and think about it before you go on to the next frame. Do not rule out any possibility, and do not worry if you do not know any math. Just put common sense to work!

So -- did you think of flipping the nickel twice in a row a good many times, and keeping track of how often it came down heads exactly twice in a row? That is exactly how gamblers estimated the chances of various hands occurring in cards, roulette odds, and other events for hundreds of years before mathematicians found more elegant -- but more complex -- methods.

Go ahead and do it. Try perhaps twenty pairs of flips, keeping track of each "OUTCOME" (remember the word). What do you find?

Flipping coins is a perfectly fine way to get an answer, just as good as any formal mathematics even if it is not as fancy. But we can do the job even faster with the computer, and it is more fun. We simply tell the computer to do the equivalent of flipping coins, by looking at a set of "RANDOM NUMBERS"; numbers from zero to nine that were produced by a process like mixing numbered balls in a bowl and pulling them out at random.

This is how we tell the computer to flip one coin twice, using the special commands that RESAMPLING STATS understands:

GENERATE  2  1,2  A
COUNT  A  =1  J
PRINT  A  J

Common sense tells you that one trial with the two coins is not enough to give you a satisfactory answer. Because the next time you flip them the number of heads might well be different than before. Obviously we need a lot more experience. Therefore, let's do it a hundred times; if that is not enough, we can do it even more times a bit later.

To repeat the operation we simply mark off the beginning and end of the "LOOP" (an important word) to be repeated, and in advance we indicate the number of repetitions to be done before the operation is ended -- we decide on a hundred repetitions, for reasons that we will discuss later.

The RESAMPLING STATS program now looks like this:

  REPEAT 100
  GENERATE 2  1,2  A
  SCORE J  Z
  END
COUNT Z  =2  K
PRINT Z K