Why Does This Probability Equation Evaluate to 0.5?

[tntcoder]

Hi,

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

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

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 can't doubt their maths.

This is the context:

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

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 I am guessing its not that simple :p

 

[statdad]

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