P&S L2 C2 S2

Any subset E of a population Q is called an EVENT. When a random draw picks a member of the set E, we say that the event E happened. If the random draw picks an element of the set Q which does not belong to E, then we say that the event did not happen,.

EXAMPLE. Consider the weather tomorrow, whether or not it will rain. Suppose the forecast is 30% chance of rain. We create a MODEL for tomorrows weather by creating a hypothetical population Q consisting of 10 members -- each of the members is a POSSIBLE WEATHER for tomorrow. Three of these members are RAIN and Seven of the members are DRY. Consider the set E to be the three rain members. The weather is picked by a simple random draw from these ten possible days [according to our model]. Then the Probability of Rain is 30% and the probability of NOT RAIN is 70%.

AXIOM: The sum of probabilities of complementary events is 100%

For any event E, the event ~E, also called not E, is the complement of E or the set of all members which do not belong to E. A random draw R must either belong to E or to ~E, which leads to the following law:

In words, we can say that one of the two event, either E or not E, must happen. The sum of the two probabilities is 100%.

In particular the event Q, which is the full population, has probability 100%. The EMPTY SET is the complement of Q, with no members, and has probability 0.