The rules and notation that were used when looking at sets can be applied to the probabilities of combined events.

The probability of an event A occurring is written as P(A).

The probability of events A and B both occurring is written

 and the probability of either A or B (or both), occurring is written

When looking at combined events, it is important to define the relationship between the events. This relationship will determine the rules that you use to combine the probabilities. You will probably already be familiar with the definitions given below.

Independent Events

If the result of one event has no bearing on the result of the other, then the events are said to be independent.

For example, the probability of rolling a 6 and picking an ace from a pack of cards. Clearly, whether you actually roll a 6 will have no bearing on the card you choose.

Dependent Events

When the result of one event affects the outcome of the other, the events are said to be dependent.

For example, the probability that it snows and the probability that you are late for school. Clearly if it snows, then traffic conditions will not be so good, making it more likely that you will be late for school.

Mutually Exclusive Events

If it is impossible for two events to both occur, then they are said to be mutually exclusive.

For example, Manchester United winning the Premiership and Leeds United winning the Premiership. Since it is impossible for both events to occur, the probability of them both happening must be zero

Complementary Events

Complimentary events cover all possibilities.

For example, Manchester United win the Premiership and Manchester United do not win the Premiership. Clearly one of these must occur, so the combined probability must equal 1.

The next page will look at the differences in combining dependent and independent events.

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