P&S L2 C2 S1

In a Population, a random draw picks all element with equal probability. For any subset of the population, the probability of a member of the subset is equal to the number of elements in that subset.

EXAMPLE: given 30 students in the class, 5 of them are LEFT handed. WHAT IS THE probability that a random draw will pick a left handed person? Answer: 5/30

it is also true that if S is the null set with no members, then P(S)=0. Also, if S is the full set S=P than P(S)=1. A random draw will always pick some member of the whole set.

Kolmogorov's Axioms:

Axiom 1: Probabilities lie between 0 and 1

More formally, suppose P is a population with N members, where N>1. Suppose R is a simple random draw from the population P. Suppose E is a subset of P. Then the probability of E is by definition the probability that the random draw R picks an element of E. This can be written as follows:

This statement is read is follows: The probability that the random draw R belongs to the set E is the ratio of #E to #P WHERE #E means the number of elements in the set E and #P means the number of elements in the population P.

Since any subset of P must have between 0 and N members, the probability that a random draw picks an element of this subset is betweeh 0 and 1,. IN FORMAL mathematical language, we write 0 <= P(S) <= 1 for all subsets S OF P.