The document defines probability as a measure of how likely an event is to occur, expressed as a ratio from 0 to 1. It discusses the basics of probability formulas and the three main types: theoretical, experimental, and axiomatic probability. Theoretical probability uses the ratio of favorable to total outcomes without experiments. Experimental probability is based on conducting actual experiments and recording results. Axiomatic probability sets axioms that apply to all probability types, including Kolmogorov's three axioms that define probability as a positive real number between 0 and 1.

2.  Probability is the measure of how likely it is some event
will occur, a number expressing the ratio of favourable
cases to the whole number or cases possible.
 The value is expressed from zero to one.
 The idea of probability is based on observation.

3. BASICS FORMULA OF PROBABILITY
Probability of event to happen P(E) = Number of
favourable outcomes/Total Number of outcomes
[Where E is event.]

4. TYPES OF PROBABILITY
Theoratical Probability
Experimental Probability
Axiomatic Probability

5. THEORETICAL PROBABILITY
The theoretical probability is defined as the ratio of the number of
favourable outcomes to the number of possible outcomes.
FORMULA OF THEORETICAL PROBABILITY
Probability of Event P(E) = No. of. Favourable outcomes/ No. of.
Possible outcomes.

6. Example of Theoratical Probability
Find the probability of rolling a 5 on a fair die
Solution:
To find the probability of getting 5 while rolling a die, an
experiment is not needed. We know that there are 6 possible
outcomes when rolling a die. They are 1, 2, 3, 4, 5, 6.
Therefore, the probability is,
Probability of Event P(E) = No. of. Favourable outcomes/ No.
of. Possible outcomes.
P(E) = 1/6.
Hence, the probability of getting 5 while rolling a fair die is
1/6.

7. EXPERIMENTAL PROBABILITY
Experimental probability, also known as Empirical probability, is
based on actual experiments and adequate recordings of the
happening of events. To determine the occurrence of any event, a
series of actual experiments are conducted.
FORMULA OF EXPERIMENTAL PROBABILITY
Probability of an Event P(E) = Number of times an event occurs /
Total number of trials.

8. Example of Experimental Probability

9. AXIOMATIC PROBABILITY
Axiomatic probability is a unifying probability theory. It sets
down a set of axioms (rules) that apply to all of types of
probability, including frequentist probability and classical
probability. These rules, based on Kolmogorov’s Three Axioms,
set starting points for mathematical probability.

10. THESE THREE AXIOMS ARE
First Axiom
The probability of an event is a positive real number,
P(E)≥0
Second Axiom
The probability of the sum of all subsets in the sample space is
P(S) = 1(OR)P(ω1)+P(ω2)+…P(ωn)=1
Third Axiom
If E1 and E2 are mutually exclusive events,
thenP(E1∪E2)=P(E1)+P(E2)
We can also see this true for P(ϕ).
Therefore, P(E∪ϕ)=P(E)+P(ϕ)=P(E)Here, P(ϕ) is a null set (or)
P(ϕ) = 0

11. APPLICATIONS OF PROBABILITY IN REAL LIFE
 Weather planning
 Sports strategies
 Insurance
 In Games
 In Politics