Consequences of the postulates

1. Let A and B be mutually exclusive events. Then the probability of their union is the sum of their individual probabilities;

that is

More generally, if are mutually exclusive events, then

2. If are collectively exhaustive events, then the probability of their union is .

Since the events are collectively exhaustive, their union is the whole sample space S and .

Example:

A drawer contains three pairs of red socks, two pairs of black socks and four pairs of brown socks. If a person in a dark room selects a pair of socks, find probability that the pair will be either black or brown. (Note: The socks are folded together in matching pairs).

Solution:

Let us define the following events

A= the selected socks are black

B= the selected socks are brown.

Since there are nine pairs of socks,

P (black) = P (A) = ; P (brown) = P (B) =

P (black or brown)= .

Example:

A day of the week is selected at random. Find the probability that it is a weekend day.

Solution:

Let

A = the selected day is Saturday

B= the selected day is Sunday

P (A)= ; P (B)= and

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