Arithmetics Probability

arithmetics probability is a measurement of uncertainty. In this arithmetic probability section we will consider chances of happening of events.

First let us see what are the common and most used terminology used in arithmetic probability.

Important Terms used in arithmetics probability

TRIAL AND EVENT: The performance of a random experiment is called a TRIAL and the outcome is an EVENT. Thus throwing of a dice would be called a trial and the result i,e falling of any one of the six numbers is an even.

let us see some of the examples of trials and events:

1) when a coin is tossed. The outcomes may be { H , T } where H is Head and T is tail.

2) when a dice is thrown, the outcome may be { 1, 2 , 3, 4, 5, 6 }

3) when a candidate appears at a certain examination. The outcomes may be  { PASS, FAIL }

4) A person is selected randomly and is asked the day of the week on which he was born. The outcomes may be { SUNDAY, MONDAY, TUESDAY, WEDNESDAY, THURSDAY, FRIDAY, SATURDAY }

PROBABILITY OF AN EVENT

Probability of an event denoted by P( E ) and is defined as

P(e) = n(E)/n(S)= no of desired events/total number of events

i,e Probability is the ratio of " The number of desired events to the Total number of events " .

Examples for arithmetics probability

let us solve a problem on arithmetics probability.

Ex 1: A dice is thrown. what is the probability that the number shown on the dice is

i) an even number  ii) an odd number iii) a number divisible by 2

sol : In all the above cases,  S = { 1, 2, 3, 4, 5, 6 }, therefore  n (S) = 6

i)  E ( an even no.) =  { 2, 4, 6 },    n( E ) = 3

therefore  P ( E ) =  n ( E ) ⁄ n ( s ) =  3 / 6 = 1/2

ii)  E ( an odd no.) =  { 1, 3, 5 },    n( E ) = 3

therefore  P ( E ) =  n ( E ) ⁄ n ( s ) =  3 / 6 = 1/2

iii)  E ( a number divisible by 2 ) = { 2, 4, 6 },    n( E ) = 3

therefore  P ( E ) =  n ( E ) ⁄ n ( s ) =  3 / 6 = 1/2