Probability

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Imagine you have a jar of 500 coins. 1 out of 500 is a coin with two heads and all the others have a tail and a head. You take a random coin from the jar and flip it 8 times. You observe heads 8 consecutive time. Are the chances that you took the coin with two heads higher than having drawn a regular coin with a head and a tail?

You have a probability of 1/500 to draw the special coin and a probably of 499/500 to draw one of the regular coints. The probability of 8 consequitves heads is 1 for the special coin and (1/2)^8 for the regular coin. Combined, that gives you a 0.2% probability to draw the special coin and flip heads 8 times (1/5001) and a probability of 0.4% to draw a regular coin and flip heads 8 times (499/5001/256). Thus, the answer is no. You are not more likely to have drawn the special coin.