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# Index of coincidence

#### Description

The index of coincidence provides a measure of how likely it is to draw two matching letters by randomly selecting two letters from a given text.

With a random piece of text, with each letter having the same chance of appearing, there is a 1/26 = 0.0385 chance of appearing.

(Note: using english alphabet with 26 letters).

The index of coincidence is defined as:

$$\mathbf{IC} = \frac{\displaystyle\sum_{i=A}^{i=Z}f_i(f_i -1)}{N(N-1)}$$

Where fi is the count of letter i (where i = A,B,...,Z) in the text, and N is the total number of letters in the text.

For testing, the index of coincidence of the text "HEREISANEXAMPLETEXT" is $$0.076$$ (3 d.p.)

#### Question

What is the index of coincidence, to 4 decimal places, of the text: "ECPTWNTTGFMGHIKGWWCNJPWRJUIJVVDQRNDPOUIVYHVWQKCHPTHLJKWXCZOCKHIGZOMIYCVHRSNZDTDUIFCRVWQKRLTOWHVNYPIIHVGMJNHV"

What is the index of coincidence, to 4 decimal places, of the text: "ECPTWNTTGFMGHIKGWWCNJPWRJUIJVVDQRNDPOUIVYHVWQKCHPTHLJKWXCZOCKHIGZOMIYCVHRSNZDTDUIFCRVWQKRLTOWHVNYPIIHVGMJNHV"