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Simple Probability Equation

  1. Nov 11, 2009 #1

    Please can someone explain to me how this probability equation evaluates to 0.5

    [tex]\frac{2^{f(n)+2}}{2^{f(n)+1}} = \frac{1}{2}[/tex]

    f(n) is essentially anything in this context.

    For me the probability evaluates to 2, but this is straight out a research paper and I cant doubt their maths.

    This is the context:

    Because there are [tex]2^{f(n)+2}[/tex] texts with length [tex]f(n)+2[/tex], the probability for a selected text with length [tex]f(n)+2[/tex] having a related
    compressed text of length ≤ f(n) is less than [tex]\frac{2^{f(n)+2}}{2^{f(n)+1}} = \frac{1}{2}[/tex]

    Please can someone explain to me where the 0.5 comes from? I can see if i turn the equation upside down it works, but Im guessing its not that simple :p
  2. jcsd
  3. Nov 12, 2009 #2


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    Homework Helper

    Make sure you've typed things correctly - otherwise the expression seems to be the reciprocal of what it should be.

    \frac{2^{f(n)+2}}{2^{f(n)+1}} = \frac{2 \times 2^{f(n)+1}}{2^{f(n)+1}} = 2

    If the original expression is the reciprocal of what you've typed, the expression does
    reduce to 1/2
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