Why is the average case time complexity same as that of the worst case in the BINARY SEARCH?

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I have derived the value for the average case for binary search and also for worst case. But i am unable to understand why they are the same.

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This question was excelently answered on the Computer Science stack exchange site here. https://cs.stackexchange.com/a/32093/89619

I cannot quote the contents of the question here, as SO does not support LaTex.

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