Editing Information content (section)

=== Fair coin toss ===
Consider the [[Bernoulli trial]] of [[coin flipping|tossing a fair coin]] <math>X</math>. The [[Probability|probabilities]] of the [[Event (probability theory)|events]] of the coin landing as heads <math>\text{H}</math> and tails <math>\text{T}</math> (see [[fair coin]] and [[obverse and reverse]]) are [[one half]] each, <math display="inline">p_X{(\text{H})} = p_X{(\text{T})} = \tfrac{1}{2} = 0.5</math>.  Upon [[Sampling (signal processing)|measuring]] the variable as heads, the associated information gain is
<math display="block">\operatorname{I}_X(\text{H})
 = -\log_2 {p_X{(\text{H})}}
 = -\log_2\!{\tfrac{1}{2}} = 1,</math>so the information gain of a fair coin landing as heads is 1 [[Shannon (unit)|shannon]].<ref name=":0" /> Likewise, the information gain of measuring tails <math>T</math> is<math display="block">\operatorname{I}_X(T)
 = -\log_2 {p_X{(\text{T})}}
 = -\log_2 {\tfrac{1}{2}} = 1 \text{ Sh}.</math>