So when you toss a fair coin 100 times, you should expect to get roughly 50 Heads and 50 Tails. That is because Heads and Tails are equally likely. The probabilities of each event – Heads and Tails – are both equal. Because they are equal, they are both given a probability of ½.

The ubiquitous coin toss is not so random after all, and can easily be manipulated to turn up heads, or tails, a Canadian study has found. Success depended on how high a coin was tossed, how quickly it was tossed it, how many times it was spun and how it was caught. …

1 in 2^100

a 1/1024 chance

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.

38.7%

Assuming a fair coin, there is a 50% chance of winning or losing on each flip. The chances of losing two times in a row is 0.5 x 0.5 = 0.25. The chances of losing 11 times in a row, in the first 11 tosses, is 0.5^11= 0.00048828125. Or about 2000 to 1 ( 1/0.00048828125 = 2048) as the article points out.

1/16

That probability is (1/2) * 5, or 1/32. Because there are two ways to get all five of one kind (all heads or all tails), multiply that by 2 to get 1/16. All of the other possibilities will result in at least one head and one tail, so the correct answer is 1 – 1/16 = 15/16.

0.19

a 6/16 chance

0.62

In probability theory and statistics, a sequence of independent Bernoulli trials with probability 1/2 of success on each trial is metaphorically called a fair coin. One for which the probability is not 1/2 is called a biased or unfair coin.

It is of course impossible to rule out arbitrarily small deviations from fairness such as might be expected to affect only one flip in a lifetime of flipping; also it is always possible for an unfair (or “biased”) coin to happen to turn up exactly 10 heads in 20 flips.

One potential problem with small clinical trials (n < 100)7 is that conventional simple randomization methods, such as flipping a coin, may result in imbalanced sample size and baseline characteristics (ie, covariates) among treatment and control groups.

We analyze the natural process of flipping a coin which is caught in the hand. We prove that vigorously-flipped coins are biased to come up the same way they started. The amount of bias depends on a single parameter, the angle between the normal to the coin and the angular momentum vector.

When a coin is pushed across a table and it slows down, that is an example of unbalanced forces. When the coin stops, the forces are in balance.

Cheat With Science: Win a Coin Toss

1. Do the flipping. You need to know which side of the coin starts faceup — you’ll be going for a specific number of flips.
2. Practice. The trick is to flip the coin the same way every time, with the same force behind your thumb.
3. Be smart. If all else fails or you’re not the flipper, choose the side that starts facing up.

There are two ways to determine if a coin is biased or fair. The most common way is to flip the coin a bunch of times and see what fraction are heads. If you only flip it 10 times and get 3 heads, there is little to conclude. But if you flip it 1000 times and get 300 heads, it almost certainly is biased.

1 : free from bias especially : free from all prejudice and favoritism : eminently fair an unbiased opinion. 2 : having an expected value equal to a population parameter being estimated an unbiased estimate of the population mean.

Most people assume the toss of a coin is always a 50/50 probability, with a 50 percent chance it lands on heads, and a 50 percent chance it lands on tails. Not so, says Diaconis. And, like a good mathematician, he’s proven it.