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What is the difference between likelihood and probability

Topics: Mathematics

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In non-math world these words can be used interchangeably, they are synonyms.
In statistics they are different: One may ask "If I were to flip a fair coin 100 times, what is the probability of it landing heads-up every time?" or "Given that I have flipped a coin 100 times and it has landed heads-up 100 times, what is the likelihood that the coin is fair?" but it would be improper to switch "likelihood" and "probability" in the two sentences.
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