### Brain Teasers

# Flipped Out

Probability
Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.Probability

If you flip 5 coins and they all come up heads, what is the probability that the 6th coin will be heads?

### Answer

1/2. The other flips have nothing to do with the 6th coin flip.Hide Answer Show Answer

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## Comments

I agree. You always have a 50% chance. However, I had an interesting arguement with a friend. Let's say you're running from one tree to another, and you're being shot at by someone who hits his target half the time. If I gave you the choice of running from tree to tree either 5 times or six times, you'd choose 5 of course, because you would like to live. There's something in our nature that tells us odds increase as we go. That's what built Vegas.

Yeah i agree its like if your playing with a dice some people tink you will get a 6 every 6 shots

RE the first comment. The odds do increase as you go. If you run from tree to tree and each time someone has a 50/50 chance of shooting you, is it not more likely you will die running 2 000 000 times each with a chance at 50/50, or if you run once at 50/50. Thats what Vegas is built on. Take the example here, the sixth coin is either 50/50 heads or tails, but what is the probability of one of the six coins coming out heads?

Re the second somment, if u play dice 6000 times, you will probably get very close to 1000 each number

we did that in math class

Good teaser, but I have seen it before, so I couldn't give it a high reading. It does stir food for thought, which is good.

Still, though. If you keep flipping heads, the probability SHOULD change, or at least, it would logically. Then there's the LUCK factor. You're rite, Vegas did that.

This is pretty easy, but fun nonetheless

cath, read my last comment on the "dogs" teaser. It was GIVEN that the first 5 throws were heads. Ignore the chances of throwing 5 heads in a row because that's irrelevant. The problem stated that it happened, so it did. Now then, the chances are 50% that the next throw will be heads.

Chamber - you are right on this one - but then Cath didn't disagree. The difference between this one and the dogs (I think, and if I'm wrong, that's now twice!) is that we don't know in the dogs question if its the first or second dog that's black. Actually, heads/tails makes it easier. Here we go then... I'm going to flip two coins. One will be heads (one dog black remember) what chance the other being heads? 4 choices. HH, HT, TH, TT yeah? One is heads. The ONLY one we can ignore is TT. Only a 1 in 3 chance we hit HH isn't there? God I'm good. And this is only my first look at this site!! Watch out all!! E-mail thanks, appreciation, worship, abuse et al to me. Cutedada@aol.com. I thank you.

When flipping a coin or rolling a dice (or die or whatever the singular is called) isn't the probability for each side (on a coin) or each number (on a dice) not equal? Because doesn't each side have a slight weight difference? or does that not really matter? I'm not sure.

piffle do you mean because a coin side might have a slightly different weight that there is more chance it landing that side? I don't know if coins are made like that, but its completely random when you flip the coin because it spins. AN imbalanced coin might spin faster, but the chance of you catching it on either side is the same.

Very Very Easy, but i liked it.

The question does not say the coins are normal and have a 50% chance of coming up heads or tails. The chance of getting 5 coins to come up head in a row are fairly low (~3% I think), so if that happened I would have to think something odd is going on (ie two headed coins, weighted coins, etc.) and would guess the next flip would be heads also. Now if the coins are all normal then of course the other reasons do not matter and the chance is still 50/50.

When you pick up a coin and start flipping it, you do not know where that coin came from or who might have flipped it before. Neither does the coin! It is an entirely different question to ask whether the next toss will be a head (50%) or whether the next 5 tosses in a row will be heads. The fact that something happens (for example someone wins a lottery - doesn't someone win it every time?) is different to whether you can predict that it will happen. If you got 1000 people all to toss 5 coins, would it be surprising if a couple of them tossed 5 heads in a row? No. The probability of 5 heads in a row is 1/32 so you would expect about 30 of them to toss 5 coins in a row. But could you pick any 1 of them and say definitely that this one would toss 5 in a row? No your chance of being right would be 1/32.

Far too easy. How did this get through the editors?

This should be in trick

There is another way to interpret this question (which would make it harder) that nobody here has considered -- we assume that each coin is 50% to land on heads. There are some number of mis-struck coins in the world, though, which have heads on both sides. Let's say 1 in 10,000 coins is double-headed. Now the probability that the next flip will be heads is determined in a Bayesian fashion -- P(double|5 heads) = (1/10000)/[1/10000 + (9999/10000)*(1/2)^5)] = 32/10031. Therefore, the probability that the next flip will be heads is (32/10031) + (1/2)*(9999/10031) = 10063/20032. Depending on how many double-headed coins you think are struck relative to fair coins, this number will obviously change.

Your answer is actually wrong. Check out this: http://homepage.ntlworld.com/barry.r.clarke/zmonty.htm

knbrain -- I think you misunderstand the application of the concepts being applied in the Monty Hall problem. To make things similar, you would have to say, "I flipped six coins. Given that at least five were heads, what is the probability that all six were?" Then the answer would be 1/6 instead of 1/2. But the way this problem is phrased, the answer is indeed 1/2, since each flip is independant.

ok i'm like 11 and got that in 2 seconds!

Well, It was easy eough to say its 50% chance all the time, but if there all in a row yeah it gonna me a smaller precent then 50%, still nice try heh.

Depending on how you look at it determines what the answer will be

Cute teaser ...but shouldn't this be in the trick section?

so so sry teaser dude

simple..

E-Z I learned this in 6th grade

P.S. don't forget to send me a message saying what subject you want me to make a quiz on!!!!

P.S. don't forget to send me a message saying what subject you want me to make a quiz on!!!!

It could be 1... the coin could be counterfeit.

Way too easy.

Assuming the coin actually has a probability of 1/2, then of course it's still 1/2. I say "of course" but if you know the history of mathematics you will know that this was not even obvious to mathematicians at one time - like so many things it's obvious to us because we were taught it.

However, in the real world we would reassess the assumption that a coin was fair after a certain point. There's a scene in Tom Stoppard's play Rosencrantz and Guildenstern Are Dead where they flip a coin and get a ludicrous run of heads, and speculate on what it means.

There is a mathematical approach to this, Baynesian probability, in which you adjust your beliefs about probability in the light of what has happened. But you don't need this very complex maths for a simple case - if someone keeps tossing heads, after a while you will conclude there is something wrong, maybe a two headed coin, making the probability well over 1/2, and refuse to bet!

However, in the real world we would reassess the assumption that a coin was fair after a certain point. There's a scene in Tom Stoppard's play Rosencrantz and Guildenstern Are Dead where they flip a coin and get a ludicrous run of heads, and speculate on what it means.

There is a mathematical approach to this, Baynesian probability, in which you adjust your beliefs about probability in the light of what has happened. But you don't need this very complex maths for a simple case - if someone keeps tossing heads, after a while you will conclude there is something wrong, maybe a two headed coin, making the probability well over 1/2, and refuse to bet!

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