 #### Explanation / Important formulas:

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.

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.

Probability of Occurrence of an Event: Let S be the sample and let E be an event. Then, P(E) = n(E) / n(S)

Results on Probability:

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)

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