BINOMIAL DISTRIBUTION

BINOMIAL DISTRIBUTION

A binomial experiment is a probability experiment that satisfies the following requirements.

1. Each trial can have two outcomes or outcomes that can be reduced to two outcomes. These outcomes can be considered as either success or failure.

2. There must be a fixed number of trials.

3. The outcomes of each trial must be independent of each other.

4. The probability of a success must remain the same for each trial.

The outcomes of binomial experiment and the corresponding probabilities of these outcomes are called binomial distribution.

Notation for the Binomial Distribution

P(S)     The symbol for the probability of success.

P(F)     The symbol for the probability of failure.

p        The numerical probability of success.

q        The numerical probability of failure.

P(S)=p   and   P(F)= 1-p-q

n        The number of trials.

x        The number of success.

Note that 0 <x<n.

Binomial Probability Formula

P(X) = n!    .p^x...q^n-x

                        ^(n-X)!X!

^{J. Santillan}

Probability Distribution and Mean, Variance and Expectation

Variable- characteristic or attribute that can assume different values.
Random Variable- a variable whose values are determined by chance.
Discrete Variables- values that can be counted.
Continuous Variable- obtain from data that can be measured rather than counted.


PROBABILITY DISTRIBUTION

• First requirement for a probability distribution: the sum of the probabilities of all events in the sample space must be equal to 1, that is SP(X)=1
• Second requirement for a probability distribution: the probability for each event is the sample space must be between or equal to 0 or 1.

G. Elio

Conditional probability

The probability that the second event B occurs given that the first event A has occurred can be found by dividing the probability that both events occurred by the probability that the first probability has occurred.

                P(A and B)

P(B/A)=

    P(A)






V.Sabusap

Addition and Multiplication Rules for Probability

Two events are mutually exclusive events if they cannot occur at the same time or they have no outcomes in common and if they cannot occur at the same time they are not mutually exclusive events.

ADDITION RULE

Addition rule 1: When 2 events A and B are mutually exclusive, the probability that A or B occurs is

P(A or B)=P(A)+P(B)

Addition rule 2: When 2 events A and B are not mutually exclusive then,

P(A or B)=P(A)+P(B)-P(A and B)

MULTIPLICATION RULE

Two events A and B are Independent events if the fact that A occurs does not affect the probability of B occurring.

P(A and B)=P(A)xP(B)

When an occurrence or outcome of the first event affects the occurrence or outcome of the second event in such a way that the probability is changed, the events are said to be dependent.

P(A and B)=P(A)xP(A/B)






C.Ordoyo