Question

What is probability? How do we find probability give examples (Explanation required clearly)​

Answer 1

Answer :-

Let us first understand some basic terms related to probability -

Experiment :- Experiment is an operation which produces well defined outcomes.

Sample space :- The set of all possible outcomes is called as sample space.

For example :- When a coin is tossed then,

Sample space = { Head , tail }

Event :- A subset of sample space is called an event.

For example :- In tossing a coin getting a head is an event.

Favourable event :- Let's understand with example -

For example : In throwing a pair of dice, A is defined by " getting 8 as the sum ". Then following elementary events are as out comes : ( 2 , 6 ) , ( 3 , 5 ) , ( 4 , 4 ) , ( 5 , 3 ) , ( 6 , 2 ). So there are 5 elementary events favourable to event A.

Probability :-

$\boxed{\sf P(A) = \dfrac{Total \:number \:of \:favourable \:outcomes}{Total \:number \:of \:possible \:outcomes}}$

Some important points for probability -

i) $\sf 0 \leq P(A) \leq 1$

ii) If, P(A) = 0, then A is called impossible event.

iii) P(A) = 1, then A is called sure event.

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

where -

P(A) = probability of occurrence of A.

$\sf P(\bar{A})$ probability of non - occurrence of A.

Examples -

Question 1 :-

A dice is thrown once. Find the probability of getting -

i) A prime number

ii) An odd number

iii) mutiple of 2 or 3

Solution :-

i) Favourable events - { 2 , 3 , 5 }

Favourable number of events = 3

Total number of events = 6

$\implies\sf Probability = \dfrac{3}{6} = \dfrac{1}{2}$

ii) Favourable events - { 1 , 3 , 5 }

Favourable number of events = 3

Total number of events = 6

$\implies\sf Probability = \dfrac{3}{6} = \dfrac{1}{2}$

iii) Favourable events - { 2 , 3 , 4 , 6 }

Favourable number of events = 4

Total number of events = 6

$\implies\sf Probability = \dfrac{4}{6} = \dfrac{2}{3}$

Question 2 :-

A coin is tossed twice. Find the probability of getting -

i) No head

ii) At least one head

Answer :-

i) Favourable outcome = { TT }

Favourable number of event = 1

Total number of event = 4

$\implies\sf Probability = \dfrac{1}{4}$

ii) Favourable outcome = { TT , TH , TH }

Favourable number of events = 3

Total number of event = 4

$\implies\sf Probability = \dfrac{3}{4}$

Answer 2

The extent to which an event is likely to occur, measured by the ratio of the favourable cases to the whole number of cases possible.One or more outcomes of an expriment makes an event.

Probability of an event= number of outcomes that makes an event/Total number of outcomes of the experiment

Suppose Question is :

• If you have a spinning wheel with 3 green sectors, 1 blue sector and 1 red sector, what is the probability of getting green sector? What is the probability of getting a non blue sector?

Solution:

=> There are total 5 sectors on the spinning wheel

=> There are 3 green sectors

Therefore Number of given outcomes=3

=> Probability of getting green sector(3 green+1 red)

Therefore Number of possible outcomes is 4

=>Probability of getting non-blue sector =4/5