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Coin flipping, coin tossing, or heads or tails is the practice of throwing a coin in the air and checking which side is showing when it lands, in order to randomly choose between two alternatives. It is a form of sortition which inherently has two possible outcomes.
The symbols H and T represent more generalised variables expressing the numbers of heads and tails respectively that might have been observed in the experiment. Thus N = H + T = h + t. Next, let r be the actual probability of obtaining heads in a single toss of the coin. This is the property of the coin which is being investigated.
Using for heads and for tails, the sample space of a coin is defined as: Ω = { H , T } {\displaystyle \Omega =\{H,T\}} The event space for a coin includes all sets of outcomes from the sample space which can be assigned a probability, which is the full power set 2 Ω {\displaystyle 2^{\Omega }} .
Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).
Recently Robert W. Vallin, and later Vallin and Aaron M. Montgomery, presented results with Penney's Game as it applies to (American) roulette with Players choosing Red/Black rather than Heads/Tails. In this situation the probability of the ball landing on red or black is 9/19 and the remaining 1/19 is the chance the ball lands on green for the ...
When people are asked to make up a random-looking sequence of coin tosses, they tend to make sequences where the proportion of heads to tails stays closer to 0.5 in any short segment than would be predicted by chance, a phenomenon known as insensitivity to sample size. [12]
They may try to produce "random" sequences by switching their actions from Heads to Tails and vice versa, but they switch their actions too often (due to a gambler's fallacy). This makes it possible for expert players to predict their next actions with more than 50% chance of success.
For example, if a typical coin is tossed and one assumes that it cannot land on its edge, then it can either land showing "heads" or "tails." Because these two outcomes are mutually exclusive (i.e. the coin cannot simultaneously show both heads and tails) and collectively exhaustive (i.e. there are no other possible outcomes not represented ...