What is a biased coin probability?

Answer 1

A biased probability is one where not every outcome has the same chance of occurring. A biased coin is one where one side, the "heads" or "tails" has a greater probability than the other of showing.

A coin which has a centre of gravity closer to the tails side than the heads side would be biased in that heads is more likely to show than tails.

The size of coin can have an effect on the probability of heads and tails - during the Royal Institute Christmas lectures in the 1990s demonstrating probability a large version of the pound coin was made to be able to allow the audience to see it being tossed - on the broadcast (and tape) version it landed and stayed on its edge! showing the probability of heads = tails ≠ ½; the probability of heads = probability of tails, but they are actually slightly less than ½ as the coin could land on its edge and stay there - with a standard size coin, if it lands on its edge it takes very little for the centre of gravity to shift outside the base of the edge and for the coin to fall over, but with a very large similar coin (ie one scaled up [proportionally] in lengths) it can take quite a bit before the centre of gravity goes outside the base if it lands on its edge which forces it to fall over (plus there will be a "significant" rise in the centre of gravity to do so, thus favouring stability on an edge which does not exist in the standard, small, sized version of the coin).

Answer 2

An UNBIASED coin is supposed to have a probability of 0.5 (50%) for either of the two possible results. A BIASED coin would be one that has any probability other than that.