In Aptitude , Probability is the ratio of wanted outcomes to the total number of possible outcomes i.e.

P(A) = \mathbf{ \frac{The Number Of wanted outcomes }{The total number Of Possible Outcomes}}

Formula & Definition for Probability

Probability is a number that reflects the chance or possibility of a particular event will occur.

Probability refers to the extent of occurrence of events. When an event occurs like throwing a ball, picking a card from deck, etc ., then the must be some probability associated with that event.

In terms of mathematics, probability refers to the ratio of wanted outcomes to the total number of possible outcomes. There are three approaches to the theory of probability, namely:

P(A) = \mathbf{ \frac{The Number Of wanted outcomes }{The total number Of Possible Outcomes}}

Basic Definition and Formula

Random Event :- If the repetition of an experiment occurs several times under similar conditions, if it does not produce the same outcome everytime but the outcome in a trial is one of the several possible outcomes, then such an experiment is called random event or a probabilistic event.

Elementary Event – The elementary event refers to the outcome of each random event performed. Whenever the random event is performed, each associated outcome is known as elementary event.

Sample Space – Sample Space refers tho the set of all possible outcomes of a random event.Example, when a coin is tossed, the possible outcomes are head and tail.

Event – An event refers to the subset of the sample space associated with a random event.

Occurrence of an Event – An event associated with a random event is said to occur if any one of the elementary event belonging to it is an outcome.

Basic Probability Formulas

Probability Range – 0 ≤ P(A) ≤ 1

Rule of Complementary Events – P(A^{C}) + P(A) =1

Rule of Addition – P(A∪B) = P(A) + P(B) – P(A∩B)

Disjoint Events – Events A and B are disjoint if P(A∩B) = 0

Conditional Probability – P(A | B) = \frac{P(A∩B)}{2}

Bayes Formula –P(A | B) = P(B | A) ⋅ \frac{P(A)}{P(B)}

Independent Events – Events A and B are independent if. P(A∩B) = P(A) ⋅ P(B).

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