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Probability and its diagrams Probability is concerned with possibility and chance. When an event (e) takes place, for example a coin is flipped the probability (P) of a given outcome occurring (e.g. a head or a tail) can be calculated. For a coin, the chance of the outcome being favourable (eg ‘heads’) is often described as 50:50 or 50%. However in probability terms we would say that it is a half (½) or 0.5. Most probability questions use fractions rather than decimals to express probabilities. Fractions are often easier to work with than decimals, especially if there are recurring numbers like 0.333333 (one-third) and 0.16666 (one-sixth). Probabilities always range from 0 (the event is impossible) to 1 (the event is certain to take place). All probabilities must fall inside this range. We can express this range of probabilities mathematically as 0 ≤ P(e) ≤ 1 meaning means that the probability of an event taking place is greater or equal to zero and less than or equal to one.

Looking at the probability for ‘heads’ we know that it is 0.5 or ½ or 1 out of 2. The general case is described by

P(e) = number of favourable outcomes number of possible outcomes

When rolling dice, the number of possible outcomes is six (1,2,3,4,5,6). The probability of throwing any chosen number, for example a 2, is one favourable outcome.

P(2) = number of favourable outcomes number of possible outcomes =

6 1

The chance of NOT getting a two is much higher than the chance of getting a two because there are five numbers that are not a two (1,3,4,5,6), so if we did not want to throw a two then

P(NOT 2) = number of favourable outcomes number of possible outcomes =

6 5

If we add the chances of getting a two to the chances of not getting a two we have

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