probability class9th

 

π Mark

Mathematics

Notes:-probability

class-9th

*INTRODUCTION

In everyday life, we come across statements such as:

(i) Most probably it will rain today.

(ii) Chances are high that the price of petrol will go up.

(iii) I doubt that he will win the race.

The words 'most probably', 'chances', 'doubt', etc., show uncertainty or

probability of occurrence of an event.

Though probability started with gambling, it is now used extensively

in science, commerce, biological sciences, weather forecasting, etc.

SOME TERMS RELATED TO PROBABILITY

EXPERIMENT:- An operation which can produce some well-defined outcomes, is

called an experiment.

Each outcome is called an event.

RANDOM EXPERIMENT :-An experiment in which all possible outcomes are known

and the exact outcome cannot be predicted in advance, is called a random

experiment.

TRIAL By a trial, we mean performing a random experiment.

EMPIRICAL PROBABILITY

Suppose we perform an experiment and let n be the total number of

trials. The empirical probability of happening of an event E is defined as

P(E) =number of trials in which the event happened/total number of trials

SOME OPERATIONS AND THEIR OUTCOMES

1. Tossing A Coin

When we toss a coin, we get either heads or tails.

2. Tossing Two Coins

When we toss 2 coins, we get:

2 heads or 1 head or 0 head.

2 tails or 1 tail or 0 tail.

3. Throwing A Die

A die (whose plural is dice) is a cubical solid having six faces,

marked as 1,2,3,4,5,6 respectively.

In throwing a die, whatever number comes on the upper face, is

called the outcome.

4. Choosing Various Types of Numbers Out of Given Numbers

Suppose counting numbers 1 to 10 are given.

If E, is the event of choosing even numbers then the favourable

outcomes are 2, 4, 6, 8, 10.

If E, is the event of choosing prime numbers then the favourable

outcomes are 2,3,5,7.