Learn Probability to crack CAT Quantitative Aptitude

Probability is one of the topics that is considered by CAT aspirants to be important. Lets understand the concept.

The Probability of an Event

To each event A (a subset of the sample space), we assign a non-negative number P(A) called the probability of event A.

Axioms of Probability

No matter how we assign probabilities to events, we assume that the following three axioms are always satisfied:

Axiom 1

For any event A, the probability P(A) of the event is a non-negative real number
0 ≤P(A)

Axiom 2

The probability of the sure event S is 1 i.e. P(S) = 1

Axiom 3

For any two mutually exclusive events A and B, the probability of their union is the sum of the probability of A and the probability of B.

Using the principle of mathematical induction, Axiom 3 can be generalized as follows:

Given any n mutually exclusive events A1,A2 ..., and An; the probability of their union is the sum of the probabilities of the individual events Ai.



The Classical Approach to Probability

The classical approach to probability theory is based on the following assumptions:

(a) There are a finite number of outcomes that are possible for the randomexperiment. In other words; the sample space has a finite number of elements, say n.

S = {s₁, s₂, ..., s_n}

(b) All the outcomes of the random experiment are equally likely. More formally, all the events consisting of a single outcome are assigned the same probability.

P({s₁) = P({s₂}) = ... = P({s_n})

Calculating Probabilities Using the Classical Approach

If we have an event A = {s₁, s₂, ..., s_k}, consisting of k outcomes,

For any event A
   


For any two events A and B



For any two events A and B



The probability of the union of three events A, B and C is


Once you have understood the concept of Probability, numericals based on this concept will involve simple applications.