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 Subject: PROBABILITY Category: Science Asked by: babyhayley50-ga List Price: \$2.00 Posted: 27 May 2005 07:34 PDT Expires: 26 Jun 2005 07:34 PDT Question ID: 526284
 ```What is the probability of getting "heads" on every throw when flipping a coin seven times? 1 in ?```
 Subject: Re: PROBABILITY Answered By: omnivorous-ga on 27 May 2005 09:08 PDT Rated:
 ```Babyhayley50 -- With an "unbiased" coin your odds of a single toss are 1/2. With two tosses, it becomes 1/2*2. With 7 tosses, it is 1/2^7 (that 2 to the 7th power) = 1/128. Not impossible, but it's a very low percentage (less than 1% of the tries). Best regards, Omnivorous-GA```
 babyhayley50-ga rated this answer: `thank you`

 Subject: Re: PROBABILITY From: toufaroo-ga on 27 May 2005 07:44 PDT
 `1 in 2^7 or 1 in 128.`
 Subject: Re: PROBABILITY From: flajason-ga on 27 May 2005 08:12 PDT
 `50%. Either you will or you won't.`
 Subject: Re: PROBABILITY From: dops-ga on 27 May 2005 08:55 PDT
 `toufaroo is right it is 1/2 to the 7th power (1/128)`
 Subject: Re: PROBABILITY From: thalaron-ga on 06 Jul 2005 12:18 PDT
 ```a more precise answear is : when u face the last toss then u'r chances are still 50-50 but in probablity when u want the specific complete event of having 7 tosses which comes up heads then the 1/128 are u'r chances.```
 Subject: Re: PROBABILITY From: andrewsanalien-ga on 15 Sep 2005 14:38 PDT
 ```I've always been confused by this question. You take your coin and flip it, having a 1/2 chance of it landing on heads. You flip it again, having a 1/2 chance of it landing on heads. So on and so forth until your 7th flip. Now assume you have managed to get 6 heads up to this point. Are the odds of this next flip landing on heads 1/2?? Within the bounds of this single flip, of course the odds are 1/2. But within the context of the seven flip run, are the odds 1/128? (1/2^7)? I'm beginning to suspect the answer lies in the depreciation of the odds with each successful flip. Can someone clarify this?? My brain hurts.```
 Subject: Re: PROBABILITY From: afmn-ga on 30 Sep 2005 20:52 PDT
 ```Probability can seem confusing but it isn't really - at this level it's just about counting and ratios. A chance of something happening is, simply, the count (or total) of what is required as a ratio of all possible outcomes. When you reach the 7th throw, the chance of a head on that particular throw is 1/2, and obviously that's because, for that throw only, a head is the one result required out of 2 possible results - and that's always the case for any particular throw. So, what you may require from one throw is different from what you may require from a series of throws. If we look at a series of throws: For two throws, the reason why HH has a probability of 1/4 isn't because we multiply 1/2 by 1/2 - that's just a method of counting. The 1/4 represents one required result (i.e. HH) from four possible results (i.e. HH, HT, TH and TT). If we throw the coin three times, the possible results are: Three heads: 1 way Two heads and one tail: 3 ways Two tails and one head: 3 ways Three tails: 1 way Total: 8 ways So the chances of getting three heads are 1/8 (and the method for calculating this quickly is (1/2)^3). But note that there are 3 ways of getting two heads and a tail, so the probability of this is 3/8. You can count in this manner all the way up to seven throws and beyond (if you have the time and patience to do it!) so that, for seven throws, you get the possibility of: 7H: 1 way 6H and 1T: 7 ways 5H and 2T: 21 ways 4H and 3T: 35 ways 3H and 4T: 35 ways 2H and 5T: 21 ways 1H and 6T: 7 ways 7T: 1 way Total: 128 ways Finally, the chances for seven heads are the same if you throw a single coin seven times, or if you throw seven coins at once, or seven people each throw a single coin, or any other combination of seven throws. That's because (as long as each throw is fair) the number of possible outcomes is always 128, and the number of times you can get seven heads is always one, so the probability of seven heads will always be 1/128. In brief, then, the odds don't "depreciate" with the number of throws: the number of possibilities increases, and how that effects the odds depends on what it is you're looking for (require), e.g. if you?re looking for two heads from two throws, the odds are lower than two heads from three throws, or from four throws, and so on.```
 Subject: Re: PROBABILITY From: afmn-ga on 30 Sep 2005 21:21 PDT
 ```Oops! That last paragraph of mine should have read "...a minimum of two heads..." Sorry.```
 Subject: Re: PROBABILITY From: readerlife-ga on 08 Dec 2005 23:54 PST
 ```I've always been confused by this question. You take your coin and flip it, having a 1/2 chance of it landing on heads. You flip it again, having a 1/2 chance of it landing on heads. So on and so forth until your 100th flip. Now assume you have managed to get 99 heads up to this point. What is the probability to get another head in the 100th toss? Theoretically, because each toss is independent, it should be again 50%. But probability theory also tells us that in the long run, the tendency should be half heads and half tails. So, we got 99 heads already, but it doesn't increase the chance of getting a tail next toss. Then, how could the probability structure of half-half be demonstrated anyway?```
 Subject: Re: PROBABILITY From: randomeh-ga on 12 Dec 2005 17:51 PST
 ```For the people who are confused maybe this will help: When I flip one coin it will either be {H} or {T} heads or tails. (50% chance of getting heads) If I flip it again and again it will always either be {H} or {T} heads or tails. (50% chance of getting heads) but if I flip 2 coins (or one coin twice) the possibilities are {HH}, {TT}, {HT} or {TH} (1 in 4 chances of flipping two heads with two coins) now if I flip 3 coins: {HHH} {HHT} {HTH} {HTT} {THH} {THT} {TTH} {TTT} or a 1 in 8 chance of flipping 3 heads with 3 coins. ....but what if I flip a fourth coin what are the odds of it too being heads? it is still going to either be {H} or {T} regardless of what the first 3 coins are. So what are the odds that all 4 coins are going to heads.....there are the above 8 combinations plus the fourth coin being heads and the above 8 combinations plus the fourth coin being tails for a total of 16 combinations of which 1 has all heads. So a one in 16 chance of being all heads. In general, with each flip there will be twice as many possible combinations, but only 1 where there is all heads so the odds of flipping n coins all heads will be 1 in 2^n. A little wordy but I hope it helps.```