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

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Terminology of probability theory


1) Sample space: Is the aggregation of all possible

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








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

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.



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