Zoom International Math League: More and more Evidence (Weekly Brain Potion Discussion)

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More and more Evidence (Weekly Brain Potion Discussion)

At lunch your friend calls you over to see the silver dollar he got while on vacation. He showed you the front (heads) and the back (tails) and said it was really fun to flip.

You watched your friend flip the coin and get tails. He flipped it again and again got tails. He said, "Wow, let's see how many times I can get tails in a row!" Third flip, tails; fourth flip, tails! In fact your friend flipped the coin ten times in a row and got all tails!

Before he flipped the coin the eleventh time, you wondered, "What is the chance that the next flip is tails?"

Please share any thoughts or questions you have below. We'll monitor the responses and give our thoughts as well!

1/2, I think, because the previous attempts don't affect the current attempt. He can get either heads or tails, and the outcomes are equally likely. And while it is still unlikely that he gets 10 tails in a row, he has a 1/2 probability for each flip.

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We have no idea if the coin is fair. This could mean the probability could be anything from 0 to 1

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um... It cant be 0. Otherwise it is impossible to get the previous 10 attempts of all heads.

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If there really was a half chance of flipping tails 10 times in a row, then the chances of flipping a tail is 1/x, where x^10 equals to 2. The problem also did mention that the coin was really fun to flip, so it is probably not a fair coin

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As stated before, we have no idea is the coin is fair. Though it seems like tails must be next, as far as we know the coin is rigged to display tails 10 times and heads on the 11th.So more information is needed to solve this problem.

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Wouldn't this just be the tenth root of 1/2? as there is a chance that the probability of tails is very low, but a much higher chance that it is very high, and it should end up x^10=1/2 on average. It could by 100%, or 1 %, but 100 is far more likely, and it balances out in the end.

so around 93.3033

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Even if the coin is fair, the way your friend flips it could be rigging it. If you start with tails up, it is more likely to be tails. With some skill, he could raise this probability.

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Assuming that the coin is fair and that they're using the same coin for the 11th flip, then the probability is 1/2 because they are independent events. Now if the coin is somehow rigged, then we do not know the outcome.

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half

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I think that the chance of flipping a tail is a half of a chance. Even though flipping 10 times, and all of them are heads, the chances of flipping heads and tails are still the same.

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The coin may not be fair

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