- What is Probability
- Why we need Probability and what is the use of it
- Terms related to Probability
- Empirical Probability
- Theoretical Probability

It is widely used in the study of Mathematics, Statistics, Gambling, Physical sciences, Biological sciences, Weather forecasting, Finance etc. to draw conclusions. Insurance companies uses this to decide on financial policies

e.g. when we coin is tossed,the possible outcome are Head and Tail.So sample space is Head and tail

2) It is a probability of event which is calculated based on experiments

Example:

A coin is tossed 1000 times, we get 499 times head and 501 times tail,

So empirical or experimental probability of getting head is calculated as

Empirical probability depends on experiment and different will get different values based on the experiment

1. Here in this probability approach, it is assumed that all the events of the experiment are equally likely

2. An event having only one outcome of the experiment is called an elementary event.

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i.e. If we three elementar event A,B,C in the experiment ,then

$P(A)+P(B) +P(C)=1$

3. The event $\bar{A}$, representing ‘not A’, is called the complement of the event A. We also say that $\bar{A}$ and A are complementary events. Also

$P(A) + P(\bar{A}=1$

4. The probability of an event (U) which is impossible to occur is 0. Such an event is called an

$P(U)=0$

5. The probability of an event ( X) which is sure (or certain) to occur is 1. Such an event is called a

$P(X)=1$

6. Probability of any event can be as

$0 \leq p \leq 1$

A dice is thrown once. What is the probability of getting a number greater than 4?

Total possible outcome=6

Favourable outcome (5,6) =2

Probability = 2/6= 1/3

Cards with numbers 2 to 101 are placed in a box. A card selected at random from the box. Find the probability that the card which is selected has a number which is a perfect square.

Total number=100

Favourable outcome ( 4,9,16,25,36,49,64,81,100) =9

Probability = $\frac {9}{100}$

A card is drawn from a well shuffled deck of 52 cards. Find the probability of getting an ace.

Total number=52

Favourable outcome =4

Probability = $\frac { 4}{52}=\frac {1}{13}$

Find the probability that a leap year selected randomly will have 53 Sundays?

No. of days in a leap year = 366 days = 52 weeks + 2 days

It implies a leap year will have 52 Sundays. In remaining 2 days, possible outcomes are:

Sun, Mon

on, Tue

Tue, Wed

Wed, Thu

Thu, Fri

Fri, Sat

Sat, Sun

Total out comes = 7 Favourable outcomes that Sunday will come in these two days = 2

Required probability = $ \frac {2}{7}$

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**Notes**-
**Assignments** -
**NCERT Solutions**

Class 10 Maths Class 10 Science