# Probability - Class 9 : Notes

**(1) An operation which can produce some well defined outcome(s) is a deterministic experiment.**

**(2) An experiment which when performed produces one of the several possible outcomes is called a random experiment.
**

**In the tossing of a coin one is not sure if a Head or Tail will be obtained, so it is a random experiment.**

*For Example:*Similarly, rolling an unbiased die is an example of a random experiment.

**(3) When we perform an experiment it is called a trial of the experiment.
**

**If a coin is tossed 10 times , then each toss is called a trial.**

*For Example:*If a die is thrown 5 times, then each throw is called a trial.

**(4) An outcome of a trial of an experiment is an elementary event.
**

**When two coins are tossed simultaneously, the possible outcomes are HH,HT, TH and TT. Any one outcome like {HH} is called an Elementary event of the sample space { HH, HT, TH, TT}.**

*For Example:***(5) A collection of two or more possible outcomes(elementary events) of an experiment is called a compound event.
**

**Consider the random experiment of tossing two coins simultaneously. If we define the event “getting exactly one head”, then HT and TH are two elementary events associated to it. So, it is a compound event.**

*For Example:***(6)An events is aid to happen in trial if any one of the elementary events(or outcomes) satisfying its conditions is an outcome.**

**(7)In n trials of a random experiments, if an event A happens m times, then the probability of happening of A is given by P(A) .
**

**A coin is tossed 1000 times with the following frequencies:**

*For Example:*Head: 455, Tail: 545

Compute the probability for each event.

**Solution:**Total number of trials = 1000

Number of heads = 455

Number of tells = 545

Let E be the event of getting a head:

P(E) = Number of head/ Total number of trials

P (E) = 455/ 1000

P(E) = 91/200

P(E) = 0.455

Let E

_{1}be the event of getting a Tail.

P(E

_{1}) = Number of Tail/ Total number of trials

P (E

_{1}) = 545/ 1000

P(E

_{1}) = 109/200

P(E

_{1}) = 0.545

Thus , Probability of occurrence of head and tail are 0.455 and 0.545 respectively.

**(8) For any event a associated to an experiment, we have **

** For Example: **As shown above example, the value of P(E) is between 0 and 1.

**(9) If are n elementary events associated to a random experiment, then**

**
**

**Two coins are tossed simultaneously 500 times with the following frequencies of different outcomes:**

*For Example:*Two heads : 95 times

One tail : 290 times

No head : 115 times

Find the probability of occurrence of each of these events.

**Solution:**Total no. of tosses = 500

No. of two heads appear = 95 times

No. of one heads appear = 290 times

No. of no head appear = 115 times

Let E

_{1}be the event of getting two heads-

P(E

_{1}) = No. of two heads appear/ No. of total tosses

P(E

_{1}) = 95/500

P(E

_{1}) = 19/100

P(E

_{1}) = 0.19

Let E

_{2}be the event of getting one tail-

P(E

_{2}) = No. of one tail appear/ No. of total tosses

P(E

_{2}) = 290/500

P(E

_{2}) = 58/100

P(E

_{2}) = 0.58

Let E

_{3}be the event of getting no head-

P(E

_{3}) = No. of no head appear/ No. of total tosses

P(E

_{3}) = 115/500

P(E

_{3}) = 23/500

P(E

_{3}) = 0.23

Here .

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