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# Quantitative Ability - Probability

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The Quantitative Ability section of CAT 2021 is very important for scoring a good percentile. It has questions from almost all section of maths. Below we are providing important formulas from one such important section - Probability. It will beneficial for your CAT 2021 preparation as well as for last minute revision.

Important Formulas:

1. Experiment: An operation which can produce some well-defined outcome is called an experiment.
2. 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:
1. Rolling an unbiased dice.
2. Tossing a fair coin.
3. Drawing a card from  a pack of well-shuffled cards.
4. Picking up a ball of certain color from a bag containing balls of different colors.

Details:

1. When we throw a coin, then either a Head (H) or a Tail (T) appears.
2. A dice is a solid cube, having 6 faces, marked 1, 2, 3, 4, 5, 6, respectively.
When we throw a dice, the outcomes is the number that appears on its upper faces.
3. 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 four honors of each unit.

There are King, Queens, and Jacks. These are all called face cards.

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

Event:

Any subset of a sample space is called an event.

Probability of Occurrence of an Event:

Let S be the sample and let E be an event.

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