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## Question

(Hope this hasn't been done before)

1. There are 10 coins on a table. 9 are normal but 1 of them has 2 heads on it (i.e. will always land on heads). Without looking you pick one at random and flip it 8 times. It lands on heads each time. What is the probability of it landing on heads the next time?

Bonus question: (UNRELATED TO THE FIRST ONE) You flip a coin 20 times and it lands on tails each time. What is more likely for it to land on next, heads or tails?

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about a 53% chance of rolling another head.

-for the bonus-

a 50% chance either way since you know you don't have the double-headed coin?

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(Hope this hasn't been done before)

1. There are 10 coins on a table. 9 are normal but 1 of them has 2 heads on it (i.e. will always land on heads). Without looking you pick one at random and flip it 8 times. It lands on heads each time. What is the probability of it landing on heads the next time?

Bonus question: (UNRELATED TO THE FIRST ONE) You flip a coin 20 times and it lands on tails each time. What is more likely for it to land on next, heads or tails?

55% Heads, 45% Tails

Bonus: Neither

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(Hope this hasn't been done before)

1. There are 10 coins on a table. 9 are normal but 1 of them has 2 heads on it (i.e. will always land on heads). Without looking you pick one at random and flip it 8 times. It lands on heads each time. What is the probability of it landing on heads the next time?

Bonus question: (UNRELATED TO THE FIRST ONE) You flip a coin 20 times and it lands on tails each time. What is more likely for it to land on next, heads or tails?

1) 55%

There is a 90% chance that you have a 50/50 chance. (.9 * .5 = .45) + a 10% chance that you have a 100% chance (.1 * 1 = .1)

.45 + .1 = .55

2) Neither is more likely, they are both, still 50/50

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Pennys are not evenly weighted so the percentages are not 50/50...they're closer to 51/49 in favor of heads

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(Hope this hasn't been done before)

1. There are 10 coins on a table. 9 are normal but 1 of them has 2 heads on it (i.e. will always land on heads). Without looking you pick one at random and flip it 8 times. It lands on heads each time. What is the probability of it landing on heads the next time?

Bonus question: (UNRELATED TO THE FIRST ONE) You flip a coin 20 times and it lands on tails each time. What is more likely for it to land on next, heads or tails?

Just a guess, but coins have no memory so every time you flip, the result is a 50/50 chance of one side or the other...

If you have 10 coins and one has 2 heads, then you have 11 heads and 9 tails or a 55% chance of it landing on heads.

For the bonus Question, it would be a 50/50 chance no matter what the prior pattern...

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Seems to me that since there was a 1/256 chance of flipping heads 8 times in a row, there's a 255/256 chance that you actually have the double heads coin. And if you don't have it, there's still a 50% chance of a heads. So, I'd say 511/512 likelihood that the next one is a heads.

This is different than the flip a normal coin 10 heads in a row and the next one is still 50% chance of a heads, because the first 8 flips does provide info suggesting the likelihood that you are holding the double heads coin. I think.

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Seems like you've all misinterpreted the OP. You flip the same coin 8 times and the flip it again. You dont keep picking different coins. Sorry if that wasn't clear .

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9 normal coins have a heads and a tails, one abnormal coin has two heads. In total, there are 9 tails, 11 heads totalling 20 sides

11/20=0.55= 55% heads comes up.

Since probability will stay the same no matter how many heads have come up in a row, the answer is still 55%

Bonus: Assuming it's a fair coin, it's a 50/50 chance.

This is my first post, hope I did it right.

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Seems to me that since there was a 1/256 chance of flipping heads 8 times in a row, there's a 255/256 chance that you actually have the double heads coin. And if you don't have it, there's still a 50% chance of a heads. So, I'd say 511/512 likelihood that the next one is a heads.

This is different than the flip a normal coin 10 heads in a row and the next one is still 50% chance of a heads, because the first 8 flips does provide info suggesting the likelihood that you are holding the double heads coin. I think.

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Ok, the odds of flipping heads again on the 9th try is equal to:

the probability that you picked a regular coin and flip 9 heads in a row,

PLUS

the probability that you picked the two headed coin and flip 9 heads in a row,

this is because these are the only two ways to achieve nine straight heads according to the parameters of the ridle.

probability of picking normal coin = .9

probability of flipping 9 heads in a row with normal coin = .00195

probability of picking normal coin and then flipping nine straight heads = .9 *.00195 = .00176

PLUS

probability of picking two headed coin = .1

probability of flipping nine heads on two headed coin = 1

probability of picking two headed coin and then flipping 9 straight heads = .1*1 = .1

so, overall probability that the next flip is heads = .100176

as for the bonus, each flip is independent and odds are 50/50

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No correct answers so far.

For those of you who said both or 50/50: are you seriously telling me that if a coin lands on tails 20 times in a row with a probability of 1/1048576 that this coin is not fake or you are throwing it properly. Clearly you would have to be stupid to think that heads would be likely to come up again.

So the answer is tails is the most likely.

It was really a common sense problem more than a maths problem.

Edited by psychic_mind
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I vote for 'either' on the both propositions! Who's with me?

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Actually when I read driterions answer I like that better than mine. If he's not right, how about al ittle push in the right direction...

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Wow, you just called all your responders stupid. It is obviously you who is lacking knowledge of statistics. you asked what the next flip is likely to be. It is an individual flip of a coin, which is always 50/50. what was flipped prior bears none on the physics of a coin flipping through the air. Yes, the odds of flipping 21 heads in a row is extremely long. However, having flipped 20 heads in a row, flipping another head is a 50/50 proposition.

Perhaps you should ckeck your facts before insulting those more intelligent than you

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Why is this not correct? ---Seems to me that since there was a 1/256 chance of flipping heads 8 times in a row, there's a 255/256 chance that you actually have the double heads coin. And if you don't have it, there's still a 50% chance of a heads. So, I'd say 511/512 likelihood that the next one is a heads.

This is different than the flip a normal coin 10 heads in a row and the next one is still 50% chance of a heads, because the first 8 flips does provide info suggesting the likelihood that you are holding the double heads coin. I think.

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No correct answers so far.

For those of you who said both or 50/50: are you seriously telling me that if a coin lands on tails 20 times in a row with a probability of 1/1048576 that this coin is not fake or you are throwing it properly. Clearly you would have to be stupid to think that heads would be likely to come up again.

So the answer is tails is the most likely.

It was really a common sense problem more than a maths problem.

So say you jump off a cliff 20 times in a row, knowing you have a 50/50 chance of surving or dying. After 20 jumps and still alive you'd be the only one dumb enough to jump the 21st time according to your thinking. When something is a clear 50/50 chance it stays that way no matter the previous outcomes. It is possible to flip heads 100 times throwing 100 different ways, and still get a 50% chance throwing a heads or tails on the 101st flip.

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Is it 0.55?

9/10 (prob of choosing fair coin) X 1/2 (prob of flipping next head) + 1/10 (prob of picking two headed coin)

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Hey, its my first post.

If we are considering the entire event, that is, there are 10 coins and one of them is a double headed coin, so we are picking one of 10 coins and tossing it 9 times, we want to know the prob of it landing heads all nine times....

(prob of picking a regular coin) X (prob of regular coin coming up heads 9 times in a row) + (prob of picking the double head coin)

i.e.: (9/10) * (1/2)^9 + 1/10

= 521/5120

= 10.18%

* opps, didn't see that 2nd page, someone has already given this answer

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I got something similar 301/2560 you have 9 time 1/512 (the probability of a head on a normal coin) plus 1/10 (the probability of a fixed coin) and you get 301/2560

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OK. First of all I wasnt insulting anybody. Sorry if it sounded like I was .

Well a few of you seem to disagree with the answer to this bonus question.

There are 2 possibilities:

1. It was a normal coin and you witnessed something extraordinary (over 1 in a million chance)

2. You were using a fake coin.

Think about it. Which is more likely? I'm sure there are plenty of fake coins out there making the second option the more likely one. I never said that that it was a fair coin.

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I thought about something: how does the 9 out of 10 play into the probability that we have a double-headed coin? if it were 9999 fair coins and one double-headed coin would we be as quick to jump to the conclusion that it is 256 times more likely that we have a double-headed coin over happening to flip 8 fair heads? I don't think this is the case. So because 511/512 does not take the 9/10 original odds of picking a fair coin into account for the calculation, it must be close, but still wrong.

As to the bonus question: I'm gonna have to go with the OP on this one. There was no assumption of fairness in the original stating of the question, so no one in their right minds would assume it were a fair coin after 20 flips. (or with that kind of luck, contrary to mathematical sanity, they should buy a lottery ticket!)

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OK. First of all I wasnt insulting anybody. Sorry if it sounded like I was .

Well a few of you seem to disagree with the answer to this bonus question.

There are 2 possibilities:

1. It was a normal coin and you witnessed something extraordinary (over 1 in a million chance)

2. You were using a fake coin.

Think about it. Which is more likely? I'm sure there are plenty of fake coins out there making the second option the more likely one. I never said that that it was a fair coin.

Do you know what the chances of a coin being fake with both sides tales is, i've never seen one.

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Odds of flipping heads is 55/45, this has been stated before. Regardless of how many iterations you have, the odds of flipping the coin still remain 55/45. The probability that you are HOLDING the double head coin drastically increase. However, since you have not changed coins, your odds of flipping heads still remains 55/45. (though the odds of holding the coin may be 511/512 or whatever was being talked about). In a logical sense, I have seen someone flip heads ten times in a row. It was bizarre and freaky, but the fact remains that the odds are still 50/50 with the coin he was holding. The same statement applies here.

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Do you know what the chances of a coin being fake with both sides tales is, i've never seen one.

I've seen a couple I think. But it doesn't have to be that. There could be many factors making the results biased.

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So say you jump off a cliff 20 times in a row, knowing you have a 50/50 chance of surving or dying. After 20 jumps and still alive you'd be the only one dumb enough to jump the 21st time according to your thinking. When something is a clear 50/50 chance it stays that way no matter the previous outcomes. It is possible to flip heads 100 times throwing 100 different ways, and still get a 50% chance throwing a heads or tails on the 101st flip.

No I wouldn't be dumb enough to jump the first time .

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