**Probability** is a numerical description of how likely an event is to occur or how likely it is that a proposition is true. Probability is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility and 1 indicates certainty. Source: *Wikipedia*

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## Videos on Probability

#### Aptitude Made Easy – Probability – 7 Tricks to solve problems on Balls and bags – Part 1

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#### Aptitude Made Easy – Probability – 7 Tricks to solve problems on Balls and bags – Part 2

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Please Read the below formula and concept every time before you start to solve the questions.

*Experiment:*An operation which can produce some well-defined outcomes is called an experiment.*Random Experiment:*An experiment in which all possible outcomes are known and the exact output cannot be predicted in advance is called a random experiment.*Examples:*- Rolling an unbiased dice.
- Tossing a fair coin.
- Drawing a card from a pack of well-shuffled cards.
- Picking up a ball of a certain colour from a bag containing balls of different colours.

*Details:*- When we throw a coin, then either a Head (H) or a Tail (T) appears.
- A dice is a solid cube, having 6 faces, marked 1, 2, 3, 4, 5, 6 respectively. When we throw a die, the outcome is the number that appears on its upper face.
- A pack of cards has 52 cards.It has 13 cards of each suit, name
*Spades, Clubs, Hearts and Diamonds*.Cards of spades and clubs are*black cards*.Cards of hearts and diamonds are*red cards*.There are 4 honours of each unit.There are*Kings, Queens and Jacks*. These are all called*face cards*.

*Sample Space:*When we perform an experiment, then the set S of all possible outcomes is called the*sample space*.*Examples:*- In tossing a coin, S = {H, T}
- If two coins are tossed, the S = {HH, HT, TH, TT}.
- In rolling a dice, we have, S = {1, 2, 3, 4, 5, 6}.

*Event:*Any subset of a sample space is called an*event*.*The probability of Occurrence of an Event:*Let S be the sample and let E be an event.Then, E S.P(E) = *n*(E). *n*(S)*Results on Probability:*- P(S) = 1
- 0 P (E) 1
- P() = 0
- For any events A and B we have : P(A B) = P(A) + P(B) – P(A B)
- If
*A*denotes (not-A), then P(*A*) = 1 – P(A).