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Notes for probability chapter of class 10 Mathematics. Dronstudy provides free comprehensive chapterwise class 10 Mathematics notes with proper images & diagram.

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**(1) In the experimental approach to probability, We find the probability of the occurrence of event by actually performing the experiment a number of times and adequate recording of the happening of event.**

**(2) In the theoretical approach to probability, we try to predict what will happen without actually performing the experiment.**

**(3) An outcome of a random experiment is called an elementary event.
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Then, and are elementary associated with the experiments of tossing of a coin.

**(4) An event associated to a random experiment is a compound event if it is obtained by combining two or more elementary events associated to the random experiment.
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**(5) An event A associated to a random experiment is said to occur if any one of the elementary events associated to the event A is an outcome.
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**(6) An elementary event is said to be favourable to a compound event A, if it satisfies the definition of the compound event.
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**(7) If there are n elementary events associated with a random experiment and m of them are favourable to an event A, then the probability of happening occurrence of event A is denoted by and is defined as the ratio
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Clearly , event A occurs if we obtain any one of 2, 4, 6 as an outcome.

Favourable number of elementary events=3

**(8) For any event A associated to a random experiment, we have
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**Proof of (ii):
**If , then A is called a certain event and A is called an impossible event, if .

If m elementary events are favourable to an event A out of n elementary events, then the number of elementary events which ensure the non-occurrence of A. i.e. the occurrence of is

**(9) The probability of a sure event is 1.
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**(10) The probability of an impossible event is 0.
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**(11) The sum of the probabilities of all the outcomes (elementary events) of an experiment is 1.
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So probability of getting head is

where m is number of time head appear And n is number of time tossing coin.

So, .

Now probability of getting tail is given by

where m is number of time tail appear and n is number of time tossing coin.

So, .

So total probability of this experiment is given by . .

Hence sum of probability of all outcomes of an experiment is always 1.

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