The basic approach statistical methods adopt to deal with uncertainty is via the axioms of probability:

- Probabilities are (real) numbers in the range 0 to 1.
- A probability of
*P*(*A*) = 0 indicates total uncertainty in*A*,*P*(*A*) = 1 total certainty and values in between some degree of (un)certainty. - Probabilities can be calculated in a number of ways.
Very Simply

Probability = (number of desired outcomes) / (total number of outcomes)

So given a pack of playing cards the probability of being dealt an ace from a full normal deck is 4 (the number of aces) / 52 (number of cards in deck) which is 1/13. Similarly the probability of being dealt a spade suit is 13 / 52 = 1/4.

If you have a choice of number of items

*k*from a set of items*n*then the formula is applied to find the number of ways of making this choice. (! = factorial).So the chance of winning the national lottery (choosing 6 from 49) is to 1.

- Conditional probability,
*P*(*A*|*B*), indicates the probability of of event*A*given that we know event*B*has occurred.

dave@cs.cf.ac.uk