We study the meaning of probability.

Probability is a branch of mathematics that studies the likelihood, or chance, of a phenomenon happening.

A random experiment is a process in which the result cannot be predicated with certainty. The result is called an outcome of the experiment. An experiment is likely to have more than one possible outcome.

A collection of outcomes is called an event. For example, rolling a dice, you get an odd number.

A measure of how likely an event E will take place is called the probability of that event, and it is denoted by P(E). Mathematically, it is defined as:

The probability of an event E, P(E), in a random experiment with equally likely outcomes is:

P(E) = (number of outcomes favorable to event E) / (total number of possible outcomes)

We also distinguish experimental probability from theoretical probability. Experimental probably refers to the probability of an event occurring when an experiment was conducted, as P(E) = (number of times E occurs) / (number of trials).

Theoretical probability, or simply  probability, P(E), is determined by noting all possible outcomes theoretically, and determine how likely the given outcome is for the event E. P(E) = (# of outcomes for event E) / (total # of possible outcomes).

Homework:

P58, #7, 8, 9, 10, 1, 14, 15, 16, 21, 23.