2010-08-13, 11:42 PM
ImagineAll Wrote:Each coin toss will remain 50/50 as each individual toss happens independently.
True. Every probability of every single coin toss is calculated with replacement; in other words, the probability of getting either a Heads or Tails is always 50%.
This is, of course, assuming that every coin toss is performed in the exact same conditions with exactly the same amount of force applied every time. The coin also has to be perfectly "unbiased".
Just because the first 10 coins turned out Heads, it doesn't make the next flip more likely to give you a Tails; you'll still have an equal chance of getting a Heads or Tails.
This doesn't mean that each and every set of coin tosses you do will always give you an equal number of Heads and Tails; all "probability" means is that as n, the number of coin tosses, approaches infinity, the ratio of the results you obtain will approach a certain value (in this case, it's 1:1). Technically speaking, it's impossible to flip a coin an infinite number of times (infinity doesn't technically exist). However you'll notice that the higher n is, the closer the ratio of Heads to Tails gets to 1:1.
This is, of course, assuming that every coin toss is performed in the exact same conditions with exactly the same amount of force applied every time. The coin also has to be perfectly "unbiased".
Just because the first 10 coins turned out Heads, it doesn't make the next flip more likely to give you a Tails; you'll still have an equal chance of getting a Heads or Tails.
This doesn't mean that each and every set of coin tosses you do will always give you an equal number of Heads and Tails; all "probability" means is that as n, the number of coin tosses, approaches infinity, the ratio of the results you obtain will approach a certain value (in this case, it's 1:1). Technically speaking, it's impossible to flip a coin an infinite number of times (infinity doesn't technically exist). However you'll notice that the higher n is, the closer the ratio of Heads to Tails gets to 1:1.