# Probability will occur. The higher the quantity of

Probability Definition

Probability is primarily the measure of the

like hood of a circumstance that will occur. The higher the quantity of an

outcome the more likely is the event will occur. Dealing with random

experiments like (tossing a fair coin) probabilities can be described

numerically by the number of outcomes divided by the total number of all

outcomes.

Terminology of probability theory

1) Sample space: Is the aggregation of all possible

outcomes.

2) Sample point: Each outcome in a sample space.

Probability theorems

Theorem (1): P (A) =1-P (A)’

Theorem (2): P (?) = 0

Theorem (3): If events A and B are such

that A ? B, then P(A) ? P(B).

Theorem (4): P (A) ? 1

Theorem (5): for any 2 events A

P (A U B) = P (a) +P (B)-P (A ? B)

–

Event is something which is likely to happen.

– Union event has elements that belongs to both A and B.

–

Intersection event contains the element which is common in A and B.

–

Complement event A’contains elements which is not in A

Types of random variables

Random variable: is a variable that assumes

numerical values related with the haphazard outcomes of experiment.

1) Discrete random variable: it has a

finite or infinite number of possible values.

Example: number of customers who arrive at

the bank from 8 -10 from Monday till Thursday.

2) Continuous random variable: it takes all

values interval of a real numbers.

Example: the time it takes for bulb to burn

out.

Types of probability distributions

What is probability distribution?

It shows what is the probability of an

event to happen.

Probability shows both:

1) Simple event such as tossing a coin.

2) Complex events such as drug effect.

Probability distribution types:

*Uniform distribution: we use this

distribution when we have no prior beliefs about the distribution of

probability overcomes or when we believe probability is equally distributed

over achievable outcomes.

*Binomial distribution: It has two possible

outcomes and each probability is between 0 & 1 and they some to 1.It can

has success & failure.

We must have two conditions in order to use

binomial distribution.

1)The probability of each outcome must be

constant for all trials.

2)Triala must be independent.

*Normal distribution: It is known by its

mean and variance.

Mean, Median and mode are equal.

The normal distribution has skewness of

zero.

Normal distribution ranged from infinitely

negative to infinitely positive.

*Lognormal distribution: is a probability whose

logarithm has a normal distribution and it has infinitely negative lower bound.

It is used to calculate expected prices.