Probability
Probability is a chance of prediction. It is quantitative measures of the chance of occurrence of a particular event.
Experiment
An operation which can produce well-defined outcomes is called an experiment.
Random Experiment
If an experiment in which all the possible outcomes are known, and exact output cannot be predicted in advance, is called a random experiment.
Examples of Performing a Random Experiment:
Tossing a fair coin
A dice is a solid cube, having 6 faces, marked 1, 2, 3, 4, 5, 6 respectively. When we throw a die, the outcomes is the number that appears on its upper face.
Rolling an unbiased dice
When we throw a coin. Then either a Head(H) or a Tail(T) appears.
Picking up a ball of certain colour from a bag containing balls of different colours.
Drawing a card from a pack of well-shuffled cards
Pack of cards that has 52 cards.
It has 13 cards of each suit, namely Spades, Clubs, Hearts, and Diamonds.
Cards of spades and club are black cards.
Cards of hearts and diamonds are red cards.
There are four honors of each suit.
These are Aces, Kings, Queens, and Jacks.
These are called face cards.
Sample Space
When we perform an experiment, then the set S of all possible outcomes is called sample space.
Examples of Sample Spaces:
(i) In tossing a coin, S = {H, T}.
(ii) If two coins are tossed, then S = {HH, HT, TH, TT}.
(iii In rolling a dice, we have, S = {1, 2, 3, 4, 5, 6}.
Event
Any subset of a sample space is called event.
Probability of Occurrence of an Event
Let S be the sample event space and E be the an event.
Then, E S.
P(E) =
n(E) n(S)
Results of Probability
(i) P(S) = 1
(ii) 0 ≤ P(E) ≤ 1
(iii) P(∅) = 0
(iv) P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
S.
