PROBABILITY - 1
Basic of Probability :-
A possibility or chances that it will happen in future is called probability.
Possibility of events happening.
Introduction
Faired Dice
Faired coin
Playing card - 52 cards
4 type ( all together is called 4 - suit )
Heart - 13 ( suit 1)
Club - 13
Spade - 13
diamond - 13
Face card - 3 in one suit so, 12 in a playing card [ J,K,Q ]
Owner cards = face card + Ace ( 16 ) —> [ A,K,Q,J ]
Knave card = [ 10 , K ,Q ] 12 cards.
APPROACH in Probability :-
Approach TYPE :-
Theoretical approach
Experimental approach or empirical approach
CLASSICAL PROBABILITY
This outcome is equally likely.
AXIOMATIC PROBABILITY
In this outcome are not equally likely
Experimental PROBABILITY :-
Depends on the past data.
Basic term in probability :-
Experiment : An operation which can produce some well-defined outcomes is called an experiment.
Outcome : An outcome of a random experiment is any one of the possible results of the experiment.
Events :- For a random experiment , an event is any possible set of outcomes.
Sample Space : The sample space of an experiment is the set of all possible outcomes or results of that experiment. The elements of a sample space may be numbers, words, letters, or symbols etc.
Symbol meaning
∩ - intersection
∪ - union
This concept will also help in SQL . ( like union, intersection, all union, etc)
Equally likely Events :-
Events are said to be equal if the probability of their occurrence ( or non-occurrence ) are equal.
These are the events which are completely distinct or same but occurrence no. is same.
Like A has 3 values and B also has 3 values.
Mutually Exclusive Events :-
Two events are said to be mutually exclusive if their intersection is a null set .
It means that when we union nothing must be common between them, or both must be distinct to each other.
Exhaustive Events :-
Events are said to be exhaustive if their union is equal to the sample state.
Both are join (union) it shows the complete dataset.
FOR US STATISTICAL / EXPERIMENTAL PROBABILITY IS MOST IMPORTANT
Experimental Probability:
Definition: experimental probability, also known as empirical or frequentist probability, is based on observed frequencies in data. It involves conducting experiments, collecting data, and calculating probabilities based on the relative frequencies of events.
Example: If you toss a coin many times and observe that it lands heads 60% of the time, the experimental probability of getting heads on the next toss is estimated to be 0.6.
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