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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 probability of 20 heads, then 1 head is 0.5 20 × 0.5 = 0.5 21; 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.
A test is performed by tossing the coin N times and noting the observed numbers of heads, h, and tails, t. 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.
Finally, the conditional probability of heads on the next flip given that the first flip was heads is the conditional probability of a heads-only coin times the probability of heads for a heads-only coin plus the conditional probability of a fair coin times the probability of heads for a fair coin, or 2/3 * 1 + 1/3 * .5 = 5/6 ≈ .8333.
Flip the coin twice. If both comes up heads or tails, end the experiment. Else, flip the coin 4 more times. This experiment has 7 types of outcomes: 2 heads, 2 tails, 5 heads 1 tail, ..., 1 head 5 tails. We now calculate the p-value of the "3 heads 3 tails" outcome.
The first time heads appears, the game ends and the player wins whatever is the current stake. Thus the player wins 2 dollars if heads appears on the first toss, 4 dollars if tails appears on the first toss and heads on the second, 8 dollars if tails appears on the first two tosses and heads on the third, and so on.
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 ...
The outer coin makes two rotations rolling once around the inner coin. The path of a single point on the edge of the moving coin is a cardioid.. The coin rotation paradox is the counter-intuitive math problem that, when one coin is rolled around the rim of another coin of equal size, the moving coin completes not one but two full rotations after going all the way around the stationary coin ...