Wednesday, 4 March 2009

More heads and tails

So the probability of tossing a coin can be complex, but you should have a rough idea of what is happening because there are only two choices. If you have heads once then heads again then the chances are 1/2 x 1/2 = 1/4. If you get heads three times the odds are 1/2 x 1/2 x 1/2 = 1/8 and throwing heads four times is 1/16.

However if you have already thrown heads three times then the odds of throwing heads again is 1/2. The coin doesn't remember what has been thrown before. It can only land on heads or tails.

To get heads twice the odds are 1/4 or 2 to the power minus 2. To get heads three times the odds are 1/8 or 2 to the power minus 3. To get heads four times the odds are 1/16 or 2 to the power minus 4.

To get heads ten times the odds are 2 to the power minus 10 or 1/1026. You have only tossed the coin ten times and you would have to do this more than 500 times to have a good chance of getting them all to be heads. If you think that is bad then think about the chances of winning the jackpot in the lottery - roughly one chance in fourteen million.

That sums it up

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