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(1) All the numbers contained in the right hand are entirely different from those in the left, i.e. there is not a single number common to both hands;—or
(2) There will be one or more numbers common to both hands.
It is impossible to foretell which of the two cases will take place.
Next, I call in a little boy of seven years, and order him to try his luck. The boy is in the same predicament as myself; he may and he may not have a common number; but it is clear that he will have a great deal less chance of having a common number in both hands; and this will be merely on account of his hands being smaller—he can grasp with them less numbers than myself. My probability of having a common number will be just as much greater than the probability of the boy's having a common number, as my hands are larger than those of the boy.
My own probability will increase with the increasing expansion of my fingers: the more I stretch them, the more numbers I shall grasp with each hand, and in this degree will increase the degree of probability of my having a common number in both hands. Now, let me put before my senses the two notions—watch, pencil: each of them is highly familiar to me; they are (
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