Uncertainty Multiplied

In our minds’ eyes last time we imagined ourselves coming to a fork in the road and seeing four paths diverge from that point.  Suppose a survey of the scene ahead now shows each path reaching a point where another decision has to be made, this time a choice between two alternatives.  Figure 4 gives us the picture so far.

The Figure illustrates the fact that the compound uncertainty, is the product of the two component uncertainties,   To convert that to an additive measure, one simply takes the logarithms to a convenient base, say and thus arrives at the not too astounding fact that the uncertainty of the first choice is bits, the uncertainty of the next choice is bit, and the total uncertainty is bits.

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