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50:50 Fifty-Fifty - what it really means

If you toss a coin, it either comes down "heads" or "tails". The chance is about 50:50, fifty-fifty, (50% versus 50%), a simple case of two possibilities with an equal chance of either. 50 percent means 50 chances out of 100, or a one in two chance, half and half. But what other things are 50:50 ? This is where some people get confused and have a misconception about it.

Take for example a typical unknown problem and its common evaluation. Supposing someone has lost their key in the garden, and they decide to search for it. As there are two possible outcomes of the search, (finding the key, or not finding it), they might say "There's two chances. It's fifty-fifty". However, that's not true. Just because there are two possible outcomes does not mean the chance if fifty-fifty. The truth is, it's only 50:50 if there are two possible outcomes which are equally likely.

You can see this with buying a ticket for the National Lottery. You could say there are only two outcomes: Winning the Lottery, or losing. Therefore it's 50:50. Clearly this is false. We all know the chance of winning the Lottery is about fourteen million to one against. So, although any ticket has two outcomes (winning or losing), the two outcomes are not equal.

Most people have enough common sense to know that for things with a tangible odds probability it's not 50:50. Dice, roulette wheels, etc, they know the odds are various fractional values. However, in more vague scenarios in the world I've seen people apply the "There's two chances. It's fifty fifty" notion to things which are approximately looking for a needle in a haystack! It's sometimes bizarre, and it may go further than it being a falsely reasoned estimate. It may be either completely missing the point, or it may be wishful thinking.

Absence of ability to compare probabilities properly could be a reason for the long-standing misconception that you're more likely to be struck by lightning than to win the Lottery

Real-life problems do have real probabilities associated with them. Even if you don't know the odds, you can still make guesses which make reasonable sense. There's some of this to be seen in the matter of placing bets on horse races. The true probabilities, if you could see them, would tend to look a bit like those which bookies give, but interestingly they'd be different from the bookies' odds because the "book" is based on where the popular vote is, not where the realistic chances are. Nevertheless, if you see a horse that's got odds of 100:1 , and you think the real probability of that horse winning is nearer to 10:1 , it might be worth placing a bet.

Other matters about the coin: The idealised coin is assumed to have precisely two sides which have an equal chance of being the result, and that there are no other possible outcomes. However, I have (on a rare occasion), seen a coin come down on the edge. It can happen.