Probability - I Summary

Let A and B be two events. Then,

where S is the sample space.

Note that simple events of a sample space are always mutually exclusive.

• Sample space: Set of all possible outcomes of a random experiment.

• Event : An event of a random experiment is defined as a subset of the sample space.

• Equally likely Events: Outcomes of a random experiment are called equally likely events, if all of these have equal frequencies.

• Exhaustive outcomes: All the outcomes of a random experiment.

• Probability of an event: P(A)

• P(A^C) = Probability of the non-occurrence of A

= 1- P(A)

• Addition Theorem: If A and B are any two events of a random

• If A, B, C are there events of a random experiment then

• If A, B and C are mutually exclusive then

• Total Probability:

P(A) = P(E₁) P(A|E₁) + P(E₂) P(A|E₂)+ … +P(E_n) P(A|E_n)

• Random variable: A real valued function 'X' defined on the sample space is called a random variable.

• Discrete random variable: A random variable which can assume only finitely or infinitely many distinct values.

• Continuous random variable: A random variable which can take any value over an interval is called a continuous random variable.

• Probability distribution of a discrete random variable is of the form