
I am having a slight problem with probabilities.

To calculate the final probability of an event p(F), we can take the product of the chance that each independent event that makes p(F) will NOT occur.
So...
p(F) = 1- ( (1-p(A)) * (1-p(B)) * (1-p(C))...(1-p(x)) )

If the chance of an event within the product occurring remains the same, we can therefore raise this probability to a power of the number of times that event occurs.
e.g. rolling a dice p(A) = 1/6 of getting a 1...
p(F) = 1 - (1- (1/6))^z 
p(F) = 1 - (1-p(A))^z tells us the probabiltity of rolling a 1 'at least once' in z number of rolls.

So then to R...

if p(A) = 0.01; z = 4; p(F) = 0.039

obviously p(F) > p(A)

however the problem arises when we use very small numbers e.g. p(B) = 1 * 10^-30
R understands this value
However when you have 1-p(B) you get something very close to 1 as you expect...but R seems to think it is 1.
So when I calculate p(F) = 1 - (1-p(B))^z = 1 to the power anything equals 1 so p(F) = 0 and not just close to zero BUT zero.
It doesn't matter therefore if z = 1*10^1000, the answer is still zero !!

Obviously therefore now p(F) < p(B)

Is there any solution to my problem, e.g.
- is it a problem with the sum (-) ? ie could I change the number of bits the number understands (however it seems strange that it can hold it as a value close to 0 but not close to 1)
-or should I maybe use a function to calculate the exact answer ?
-or something else

Any help greatly appreciated
Mark
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