The document outlines the axiomatic approach to probability, defining key concepts such as sample space, probability as a real-valued function, and the axioms that govern it. It explains that the probability of any event is non-negative, that the sum of probabilities of mutually exclusive events equals the probability of their union, and highlights the properties of exhaustive and mutually exclusive events. The author, Dhruv Sethi, offers contact information for private or group tutoring.

1. Maths topic for
Probability:
Axiomatic
approach to
probability
By Dhruv Sethi;
dhrsethi1@gmail.com/+91 9310805977
11th Grade

2. Axiomatic approach
• Let S be the sample space of a random experiment.
• The probability P is a real valued function whose domain is the power set
of S and range is the interval [0,1] satisfying the following axioms:
i. For any event E, P (E) ≥ 0
ii. P(S) = 1
iii. If E and F are mutually exclusive events, then P(E ∪ F) = P(E) + P(F)

3. Axiomatic approach
• It follows from the axioms that P(𝛟) = 0 as can be seen below:
P(E ∪ 𝛟) = P(E) + P(𝛟) (Since E and 𝛟 are disjoint)
P(E) = P(E) + P(𝛟) => P(𝛟) = 0
It also follows that
• 0 ≤ P(wi) ≤ 1 for each wi ∈ S
• P(w1) + P(w2) + … + P(wn) = 1
• For any event A, P(A) = ΣP(wi), wi ∈ A

4. Mutually exclusive and Exhaustive Events
• In general, if E1, E2, E3, …, En are n events of a sample space S and if E1 ∪
E2 ∪ E3 ∪ … ∪ En = S, then E1, E2, …, En are called exhaustive events.
• Additionally, if Ei ∩ Ej = 𝛟 for i ≠ j i.e. events Ei and Ej are pairwise
disjoint
• Then events E1, E2, …, En are called mutually exclusive and exhaustive
events

5. Exhaustive Events
• You can contact me for private or group tuitions from the details below
• By Dhruv Sethi: +91 9310805977/dhrsethi1@gmail.com
• Whatsapp: +91 8291687783