Probability :- It is measurement of uncertainty. In this chapter chances of the happening of events are considered.
Probability is important for business and economics situation and it also used by us in our personal life.
Event :- It is the correrstone or the bottomline of probability. Therefore the first objective while trying to solve any question in probability is to define the event.
The probability of an event is defined as -
$\frac{Number\; of\; ways\; in\; which\; the\; event\; occures}{Total\; number\; of\; outcomes\; possible}$
This means that the probability of any event can be got by counting the numerator and denominator independently.
The use of Conjection AND :- Whenever we use AND as the natural conjection joining two separate parts of the events, we replace AND by the Multiplication sign.
The use of Conjection OR :- Whenever we use OR as the natural conjection joining two separate parts of the events, we replace OR by the addition sign.
Some Important Considerations While Defining Event :-
Random Experiment :- An experiment whose outcome has to be among a set of events that are completely known but whose exact outcome is unknown is a random experiment.
For eg. :- Tossing of a coin.
Sample Space :- This is defined in the context of a random experiment and denotes the set representing all the possible outcomes of the random experiments.
Foe eg. :- Sample Space when a coin is tossed is ( head, tail ).
Equally Likely Events :- If two events have the same probability they are called equally likely events.
For eg. :- In a throw of a dice, the chance of 1 showing on the dice is equal to 2, is equal to 3 is equal to 4 is equal to 5 is equal to 6 appearing on the dice.
Exhaustive Set of Events :- A set of events that includes all the possibilities of the sample space is said to be an exhaustive set of events.
For eg. :- In a throw of a dice the number is less than three or more than or equal to three.
Independent Events :- An event is described as such if the occurance of an event has no effect on the probability of the occurence of another event.
For eg. :- If the first child of a couple is a boy, there is no effect on the chances of the second child being a boy.
Probability is important for business and economics situation and it also used by us in our personal life.
Event :- It is the correrstone or the bottomline of probability. Therefore the first objective while trying to solve any question in probability is to define the event.
The probability of an event is defined as -
$\frac{Number\; of\; ways\; in\; which\; the\; event\; occures}{Total\; number\; of\; outcomes\; possible}$
This means that the probability of any event can be got by counting the numerator and denominator independently.
The use of Conjection AND :- Whenever we use AND as the natural conjection joining two separate parts of the events, we replace AND by the Multiplication sign.
The use of Conjection OR :- Whenever we use OR as the natural conjection joining two separate parts of the events, we replace OR by the addition sign.
Some Important Considerations While Defining Event :-
Random Experiment :- An experiment whose outcome has to be among a set of events that are completely known but whose exact outcome is unknown is a random experiment.
For eg. :- Tossing of a coin.
Sample Space :- This is defined in the context of a random experiment and denotes the set representing all the possible outcomes of the random experiments.
Foe eg. :- Sample Space when a coin is tossed is ( head, tail ).
Equally Likely Events :- If two events have the same probability they are called equally likely events.
For eg. :- In a throw of a dice, the chance of 1 showing on the dice is equal to 2, is equal to 3 is equal to 4 is equal to 5 is equal to 6 appearing on the dice.
Exhaustive Set of Events :- A set of events that includes all the possibilities of the sample space is said to be an exhaustive set of events.
For eg. :- In a throw of a dice the number is less than three or more than or equal to three.
Independent Events :- An event is described as such if the occurance of an event has no effect on the probability of the occurence of another event.
For eg. :- If the first child of a couple is a boy, there is no effect on the chances of the second child being a boy.
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