Editing Gambler's fallacy (section)

===Why the probability is {{sfrac|1|2}} for a fair coin===
If a fair coin is flipped 21 times, the probability of 21 heads is 1 in 2,097,152. The probability of flipping a head after having already flipped 20 heads in a row is {{sfrac|1|2}}. Assuming a fair coin:
* The probability of 20 heads, then 1 tail is 0.5<sup>20</sup> × 0.5 = 0.5<sup>21</sup>
* The probability of 20 heads, then 1 head is 0.5<sup>20</sup> × 0.5 = 0.5<sup>21</sup>

The probability of getting 20 heads then 1 tail, and the probability of getting 20 heads then another head are both 1 in 2,097,152. When flipping a fair coin 21 times, the outcome is equally likely to be 21 heads as 20 heads and then 1 tail. These two outcomes are equally as likely as any of the other combinations that can be obtained from 21 flips of a coin. All of the 21-flip combinations will have probabilities equal to 0.5<sup>21</sup>, or 1 in 2,097,152. Assuming that a change in the probability will occur as a result of the outcome of prior flips is incorrect because every outcome of a 21-flip sequence is as likely as the other outcomes. In accordance with [[Bayes' theorem]], the likely outcome of each flip is the probability of the fair coin, which is {{sfrac|1|2}}.