Probability Theory

I. Probability Theory * A branch of mathematics concerned with the analysis of random phenomena. The outcome of a random event cannot be determined before it occurs, but it may be any one of several possible outcomes. The actual outcome is considered to be determined by chance. * The word probability has several meanings in ordinary conversation. Two of these are particularly important for the development and applications of the mathematical theory of probability. One is the interpretation of probabilities as relative frequencies, for which simple games involving coins, cards, dice, and roulette wheels provide examples. * It is the likeliness of an event happening based on all the possible outcomes. The ratio for the probability of an event 'P' occurring is P (event) = number of favorable outcomes divided by number of possible outcomes.
Example:
A coin is tossed on a standard 8×8 chessboard.
What is the theoretical probability that the coin lands on a black square?

Choices:
A. 0.5
B. 0.25
C. 0.42
D. 0.6

Correct answer: A

Solution:

Step 1: Theoretical probability = number of favorable outcomes / number of possible outcomes.

Step 2: The probability of the coin lands on the black square is 32.

Step 3: Total number of outcomes = 64.
Step 4: P (event) =

Step 5: == 0.5

Step 6: The theoretical probability that the coin lands on a black square is 0.5.

A. Permutation and Combination

* The various ways in which objects from a set may be selected, generally without replacement, to form subsets. This selection of subsets is called a permutation when the order of selection is a factor, a combination when order is not a factor. By considering the ratio of the number of desired subsets to the number of all possible subsets for many games of chance in the 17th century * The French mathematicians Blaise Pascal and Pierre de Fermat gave impetus to the development of combinatorics and probability theory. *