PROBABILITY

• Prepared by:
• EKTA SHAKYA
• TGT Mathematics
• JNV TIRAP
• ARUNACHAL PRADESH

​

�Introduction:��In everyday life, we come across statements such as� (1) It will probably rain today.��� (2) I doubt that he will pass the test. � (3) Most probably, Kavita will stand first in the annual examination.� (4) There is a 50-50 chance of India winning a toss in today’s match. ��

2

The concept of probability developed in a very strange manner. In 1654, a gambler Chevalier de Mere, approached the well-known 17th century French philosopher and mathematician Blaise Pascal regarding certain dice problems. Pascal became interested in these problems, studied them and discussed them with another French mathematician, Pierre de Fermat. Both Pascal and Fermat solved the problems independently. This work was the beginning of Probability Theory. ��

WHAT IS PROBABILITY ?

• PROBABILITY IS THE MEASURE OF VARIOUS PHENOMENON, NUMERICALLY

4

�

In probability we frequently use the term ‘experiment’.

There are two types of experiments:

1. Deterministic experiment
2. Random experiment

​

(i) Deterministic experiments- The experiments which have only one possible result .

Ex- an experiment that the Sun rises from the east.

​

(ii) Random experiments – An experiment whose result is uncertain

( an experiment whose all the outcomes are known but whose exact outcome is unknown).

Ex- an experiment conducted to toss a coin

​

5

​

TRIAL :

A trial is an action which results in one or several outcomes.

example- When we toss a coin the work of tossing a coin is a trail

OUTCOMES :

All the possible results of an experiment are known as outcomes

Example - when we toss a coin outcomes are head and tail

EVENT:

An event is the collection of outcomes of an experiment to which a probability is assigned.

Ex- when we throw a die outcomes are 1,2,3,4,5,6

There are many events- an event of getting an even number

• - An event of getting an odd number
• - an event of getting a number less than 4 pop

6

​

​

IMPOSSIBLE AND SURE EVENTS :

​

• Equally likely events:

​

• equally likely events are the events that have the same theoretical probability of occurring.

​

• Each numeral on a dice is equally likely to occur when the dice is tossed.

7

​

The probability of an impossible event is 0 and the probability of a sure event is 1

8

9

Ex 2 : Find the probability of getting a head when a coin is tossed once. Also find the probability of getting a tail.

​

Sol: Sample space = { H , T }

P(Head)=1/2

P(Tail)=1/2

​

​

​

​

10

Example 3

11

Example 4

• A

12

PISA RELATED QUESTION From a well shuffled pack of 52 playing cards one card is drawn at random,find the probability of getting�(a) a black card�(b) a red face card�(c) an ace card�(d) a black card with a number 10

13

14

Face cards

Ace cards

Red cards

Black cards

P(black cards)=26/52

P(red face card)=6/52

P(an ace card)=4/52

HOME WORK

15

1. A coin is tossed 500 times and we get

Heads : 285 times and tails : 215 times .

When a coin is tossed at random , what is the probability of getting

(i) a head? (ii) a tail

2) In a survey of 200 ladies , it was found that 142 like coffee , 58 dislike it.

Find the probability that a lady chosen at random

1. Likes coffee , (ii)dislikes coffee

​

​

3. In a cricket match , a batsman hits a boundary 6 times out of 30 balls he plays . Find the probability that he did not hit a boundary

​

• A bag contains 5 red, 8 black , and 7 white balls . one ball is chosen at random . What is the probability that the chosen ball is black ?

​

5) It is known that a box of 800 electric bulbs contains 36 defective bulbs.One bulb is taken at random out of the box. What is the probability that the chosen bulb is non defective .

That was all for the chapter of probability hope you got a nice learning experience from my presentation��THANK YOU

16