Flipped Out
Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.
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.
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Comments
Don Ray
Dec 08, 2001
 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. 
Rosej0
Dec 18, 2001
 Yeah i agree its like if your playing with a dice some people tink you will get a 6 every 6 shots 
cathalmccabe
Mar 11, 2002
 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? 
cathalmccabe
Mar 11, 2002
 Re the second somment, if u play dice 6000 times, you will probably get very close to 1000 each number 
shortangel
Mar 15, 2002
 we did that in math class 
Captbob61
Mar 20, 2002
 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. 
ANDREWPHAM
Mar 27, 2002
 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. 
bighippo4
Apr 04, 2002
 This is pretty easy, but fun nonetheless 
chamber44
May 17, 2002
 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. 
Andy1608
May 21, 2002
 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!! Email thanks, appreciation, worship, abuse et al to me. Cutedada@aol.com. I thank you. 
piffle
May 30, 2002
 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. 
cathalmccabe
Aug 22, 2002
 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. 
bigsurf18
Oct 11, 2002
 Very Very Easy, but i liked it. 
electronjohn
Dec 04, 2002
 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. 
jimbo
Mar 12, 2003
 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. 
PhilDunphy
Mar 20, 2003
 Far too easy. How did this get through the editors? 
horse_luver
Apr 13, 2003
 This should be in trick 
tsimkin
Nov 23, 2004
 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 misstruck coins in the world, though, which have heads on both sides. Let's say 1 in 10,000 coins is doubleheaded. Now the probability that the next flip will be heads is determined in a Bayesian fashion  P(double5 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 doubleheaded coins you think are struck relative to fair coins, this number will obviously change. 
knbrain
Dec 23, 2004
 Your answer is actually wrong. Check out this: http://homepage.ntlworld.com/barry.r.clarke/zmonty.htm 
tsimkin
Dec 27, 2004
 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. 
cmt1214
May 20, 2005
 ok i'm like 11 and got that in 2 seconds! 
Frost1250
Jul 08, 2005
 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. 
trumpetsgirl
Oct 11, 2005
 Depending on how you look at it determines what the answer will be 
teen_wiz
Feb 09, 2006
 Cute teaser ...but shouldn't this be in the trick section? 
coltonr1
Mar 15, 2006
 so so sry teaser dude

brainjuice
Mar 31, 2006
 simple.. 
flowergirl1219
Jun 27, 2007
 EZ 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!!!! 
Starriddler
Oct 13, 2007
 It could be 1... the coin could be counterfeit. 
Quickq
Aug 02, 2008
 Way too easy. 
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