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## Basic Statistical methods -- Probability

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