EDA CHAP2

probability

IT is simply how likely an event is to happen or the likelihood or chance of an event occurring.

Experiment

is used to describe any process that generates a set of data

Event

consists of a set of possible outcomes of a probability experiment. Can be one outcome or more than one outcome.

Simple event

an event with one outcome.

Compound event

an event with more than one outcome

sample space

the set of all possible outcomes or results of a random experiment. (S)

EVENT

it is the subset of this sample space and it is represented by letter E

null space

is a subset of the sample space that contains no elements and is denoted by the symbol . It is also called empty space.

Intersection of events

The intersection of two events A and B is denoted by the symbol A U (na baliktad) B. It is the event containing all elements that are common to A and B.

Mutually Exclusive Events

if they have no elements in common.

Union of Events

the event containing all the elements that belong to A or to B or to both and is denoted by the symbol A U B.

Compliment of an Event

The ———— A with respect to S is the set of all elements of S that are not in A and is denoted by A’.

Probability of an Event

sample space and events play important roles in probability. Once we have sample space and event, we can easily find the probability of that event. We have following formula to find the probability of an event.

Multiplicative Rule

Suppose you have j sets of elements, n1 in the first set, n2 in the second set, ... and nj in the jth set. Suppose you wish to form a sample of j elements by taking one element from each of the j sets.

Permutation Rule

Given a single set of n distinctively different elements, you wish to select k elements from the n and arrange them within k positions.

Partitions rule

Suppose a single set of n distinctively different elements exists. You wish to partition them into k sets, with the first set containing n1 elements, the second containing n2 elements, ..., and the kth set containing nk elements.

Combinations Rule

A sample of k elements is to be chosen from a set of n elements.

mutually exclusive or disjoint

Two events are ———- if they cannot occur at the same time.

conditional probability

The probability that Event A occurs, given that Event B has occurred, is called a ——-. It is denoted by the symbol P (A|B).

complement

The ——— of an event is the event not occurring. The probability that Event A will not occur is denoted by P (A').

intersection

The probability that Events A and B both occur is the probability of the——- of A and B. The probability of the intersection of Events A and B is denoted by P (A ∩ B). If Events A and B are mutually exclusive, P(A ∩ B) = 0.

union

The probability that Events A or B occur is the probability of the—— of A and B. The probability of the union of Events A and B is denoted by P(A ∪ B).

dependent

independent

If the occurrence of Event A changes the probability of Event B, then Events A and B are ——-. On the other hand, if the occurrence of Event A does not change the probability of Event B, then Events A and B are ——-.

Dependent

Two outcomes are said to be dependent if knowing that one of the outcomes has occurred affects the probability that the other occurs. (rule of multiplication)

Conditional Probability

an event B in relationship to an event A is the probability that event B occurs after event A has already occurred. The probability is denoted by 𝑃(𝐵|𝐴) (rule of multiplication)