John Hawks introduktion till informationsteori och genetik

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If we were not uncertain at all, the probability of one outcome would be 1 and the other would be zero. For instance, if we had a two-headed coin, we would be absolutely certain of flipping heads. Naturally, a definition of uncertainty should assign zero to the case in which we already know the outcome. But for a fair coin, we have a probability of 0.5 for one outcome, and a probability of 0.5 for the other. We are uncertain, and our measure of uncertainty should have a positive value in this case, whatever unit we may choose. Now suppose we have a nucleotide of DNA. It may be adenine, guanine, cytosine or thymine, each with probability 0.25 (1/4). How many coin flips would give us the same amount of uncertainty?