Probability

Definitions:

1. Random Experiment

• also called a statistical experiment
• an experiment in which the results will not be the same, even though the conditions or processes of doing it are nearly identical

2. Sample Space

• denoted by S
• the list of all possible outcomes in a random experiment

3. Event

• a subset of a sample space (S) denoted by capital letters such as A, B,..., Z.

I. Probability

            If an experiment can result in any one of n different equally likely outcomes, and if exactly m of these ways correspond to event A, then the probability of event A is:

Examples:
1. What is the probability of drawing a king from a deck of playing cards?
2. If a die is rolled, what is the probability that the
result is an even number?
3. If two dice are rolled, what is the probability that the sum of the numbers is less than 10? 

II. Properties of Probability

III. Laws of Probability

A. General Addition Rule

where A and B are any two events.

Example:
1. In a single draw from a deck of playing cards, find the probability of drawing each of the following.
a. an ace or a king
b. club or a face card

2. A box contains 5 balls wherein 3 are white and 2 are black. What is the probability of getting a white or a black ball in a single draw?


B. Multiplication Rule

a. For independent events:

b. For dependent events:

where P(B/A) is the conditional probability that B occurs given A had.

Example:

1. A box contains 5 balls wherein 3 are white and 2 are black. Now, 2 balls are drawn from the box successively, what is the probability that both balls drawn are black if

a. there is replacement
b. there is no replacement

2. The students in a class are selected at random, one after the other, for an examination. Find the probability that the boys and girls are seated alternately if:

a. the class has 4 boys and 3 girls
b. the class consists of 3 boys and 3 girls