# Formulas For Probability

## Formulas For Probability

In Aptitude , Probability is very Important Topic. In this Page Formulas for Probability is given.

Probability is the ratio of wanted outcomes to the total number of possible outcomes i.e. P(A) = $\mathbf{ \frac{\text{The Number of wanted outcomes }}{\text{The total number of Possible Outcomes}}}$

### 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: Classical Approach , Relative Frequency Approach , Subjective Approach.

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(AC) + 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) = $\frac{P(A∩B)}{P(B)}$
• Bayes Formula – P(A | B) = $\frac{P(B|A). P(A)}{P(B)}$
• Independent Events – Events A and B are independent if. P(A∩B) = P(A) ⋅ P(B).

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