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Given a probability, p, of an event occurring,
we know that the amount of information that

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you get from being told that a particular
event occurred is log2(1/p).

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Using that information, let's try to answer
the following questions.

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Someone picks a name out of a hat known to
contain the names of 5 women and 3 men, and

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tells you a man has been selected.

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How much information have they given you about
the selection?

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The probability of a man being selected in
this problem is 3/8.

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So the amount of information that you have
been given

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is log2(1/(3/8)) = log2(8/3).

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Another way to think about this is that if
you start off with N choices, and the additional

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information that you are given reduces your
choices to M, then the amount of information

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that you have been given is log2(N/M).

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In this example N = 8 because that is the
original number of choices.

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The reduced number of choices once you are
told that a man has been selected is 3, so

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M = 3.

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This means that the amount of information
you received is log2(8/3).

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For the second question, you are asked to
guess a random 4-bit 2's complement number.

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I then tell you that the number is greater
than 0.

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How much information have you been given?

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For this problem the original number of choices
is the number of permutations of 4 binary

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bits which is 16, so N = 16.

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Once you are told that the number is greater
than 0, this reduces your choice to 7, so

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M = 7.

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That means that the amount of information
that you have been given is log2(16/7).