Maths formulas # 04 :)

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PROBABILITY

1. Experiment:

An operation which can produce some well-defined outcomes is called an experiment.

2. Random Experiment:

An experiment in which all possible outcomes are know 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 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.

3. Sample Space:

When we perform an experiment, then the set S of all possible outcomes is called thesample 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}.

   4. Event:

                  Any subset of a sample space is called an event.

5. Probability of Occurrence of an Event:

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

P(E) =	n(E)	.
	n(S)