
Re: say I flip a coin 100 times...
Posted:
Apr 13, 2005 11:29 AM


Ralph Hartley wrote: > ken quirici wrote: >> There are 1M people and 100 coins. There are 2**100 possible >> sequences of 100 coins. The chance that 1 out of the 1M will flip >> the same sequence as you is (with ** indicating exponentiation) >> >> 1M * (2**100) (if I remember correctly you add the >> probabilities of independent events >> to get the probability that they will >> all occcur). > You *multiply* the probabilities of independent events to get the > probability that they will all occur. (What you said was wrong, but what > you *did* was correct).
Surely not. 2^{100} is about 8*10^{31}. If he had 10^31 people taking part in the experiment, this would make the probability of a match about 8, an unlikely result even on sci.math.
I get a sequence of 100 heads or tails. One million other people each do the same. For each of them, the probability of having the same sequence as me is 1/2^100. Thus, for each of them, the probability of having a different sequence from me is 12^{100}. Then the probability of all of them having a different sequence from me is (12^{100})^1000000.
So, let's see what this gives.
ln((12^{100})^1000000) = (OK, approximately) ln(18*10^{31})^1000000) = 1000000*8*10^{31} = 8*10^{25}
which is pretty indistinguishable from 0, so its exponential is damned close to 1. The probability of all sequences being different from mine is very near 1, so the probability of somebody's sequence matching mine is pretty much 0.
Now, if we had about 10^31 people doing this, then the log of the probability of them all being different would be 0.8, whose exponential is about 0.45, so the probability of somebody having a matching sequence is about 0.55.
 Rob

