# Probability - Class 10 : Notes

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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**Consider the random experiment of tossing coin. The possible outcome of this experiment are head(H) and tail (T). if we define = getting head(H), = getting tail (T)**

*For Example:*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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**In a single throw of a die, the event “getting an even number” is a compound event as it is obtained by combining three elementary events, namely 2, 4, 6.**

*For Example:***(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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**Consider the random experiment of throwing an unbiased die. Let A denote the event “getting an even number ”. Elementary events associated to this event are 2, 4, 6. Now, suppose that in a trail the outcome is 4, then we say that the event A has occurred. In another trail , let the outcome be 3, then we say that the event A has not occurred.**

*For Example:***(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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**Consider the random experiment of two coins are tossed simultaneously and A is an event associated to it defined as “getting exactly one head”. We say that the event A occurs if we get either HT or TH as an outcome. So, there are two elementary events favourable to the event A.**

*For Example:***(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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**i.e.,**

**Let A denote the event “getting an even number”**

*For Example:*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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**(i) (ii)**

**Proof of (i):**

**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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**sun is rising from the east. this is a sure event. so probability of sure event is 1**

*For Example:***(10) The probability of an impossible event is 0.
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**suppose the sun is rising from the west. this event is impossible event so probability of impossible event is always 0.**

*For Example:***(11) The sum of the probabilities of all the outcomes (elementary events) of an experiment is 1.
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**Suppose in experiment of tossing coin 10 times 6 time head appear and 4 times tails appear.**

*For Example:*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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