Probability

To calculate the probability of an event, we need to know the number of successful outcomes (e.g. the number of red counters in a bag) and divide it by the total number of outcomes (e.g. the total number of counters in a bag). The result will always be between 0 and 1 – if not, check your working!

For a single event, it either happens or it doesn’t – so the probability of it happening, P(happens) added to the probability of it not happening, P(not happens) will always equal 1.

Things start to get interesting when there are two events. Events are INDEPENDENT if the outcome of one does not affect the outcome of the other – if I toss a coin and roll a dice, the result of the coin toss will have no bearing on the dice roll. If I take a card from a pack of playing cards, and don’t replace it, then the outcome of the second card drawn is affected by the first card, and so these two events are not independent.

Two events are MUTUALLY EXCLUSIVE if they cannot happen at the same time. In a coin toss, I can’t get both a head and a tail in one toss, so these events are mutually exclusive.