1. the so-called “classical probability concept” is nothing more than what you’ve heard before called “equally likely outcomes”... In many experiments, the sample space consists of n outcomes each having probability 1/n (so they are all equally lilkely). In this specific case then, we have the following way to compute P(A) for any event A:
But beware of doing this when the sample space is not equally likely!!

2. See example on p. 66: there are 20 tires, 3 of which are defective
See example on p.66: there are 20 tires, 3 of which are defective. choose 4 tires at random.
what is P(exactly 1 of the 4 is defective)?
Solution: all 20C4 = (use TI-83)
choices of 4 tires from 20 are equally likely. there are 3C1 17C3 = 3 (680) = of these ways that have exactly 1 defective tire and 3 non-defective tires (use Theorem 3.1). So,

3. the other important idea in section 3
the other important idea in section 3.3 is that P(A) can be approximated by the relative frequency of occurrence of A in a large number of repetitions of the experiment that gives rise to A . This is called the relative frequency approach to probability and it works in many applications... we will use this to estimate some probabilities when we do simulations using the software package R.

4. Axioms of Probability. For events A, B:
0 <= P(A) <= 1
P(S) = 1, where S is the sample space
P(A or B) = P(A) + P(B), if A,B are mutually exclusive.
There are other results that follow from these:
#3 can be extended to more than two mutually exclusive events (Theorem 3.4) and this can be used to show that P(A) = sum of the probs. of the simple events in S that make up A. If A, B are not mutually exclusive, then #3 must be modified as follows:
Theorem 3.6: If A & B are any events in S, then
P(A or B) = P(A) + P(B) – P(A and B). (For the proof, draw a Venn diagram to justify why this might be true...).
We also have the “not” rule:
P(not A) = 1 – P(A)

5. HW finish reading sections 3.4 and 3.5 – pay attention to the examples
on p do # , 3.35, 3.38, 3.41, 3.46, 3.48, 3.49, 3.51, 3.52
quiz on counting and probability coming soon...