Question

A bag ticket marked with numbers 179, 180, 172, 127, 155, 115, 143, 122, 175, 222, 232, 162, 112, 136, 192, 182, 174, 132, 32, 131. A ticket is drawn at random. Find the probability that the ticket drawn has an even digit at ten’s place.
$\left( A \right)\dfrac{7}{{19}}$
$\left( B \right)\dfrac{3}{{20}}$
$\left( C \right)\dfrac{7}{{20}}$
$\left( D \right)\dfrac{6}{{19}}$

Answer 1

Hint – In this particular question use the concept that a number is always starting from a unit place there after ten’s place there after hundred places there after a thousand places and so on. So using this first calculate the numbers from the given numbers which have even ten’s place , so use this concept to reach the solution of the question.

Complete step-by-step answer:
Given data:
The number of tickets available in a bag having a unique number on the ticket are
179, 180, 172, 127, 155, 115, 143, 122, 175, 222, 232, 162, 112, 136, 192, 182, 174, 132, 32, 131.
So as we see there are 20 tickets in a bag.
So the total number of outcomes = 20
Now we have to find the probability that the ticket drawn has an even digit at ten’s place.
So as we know that a number is always starting from a unit place there after ten’s place there after a hundred places there after a thousand places and so on.
For example: consider a number xyz, in which z is a unit place, y is a ten’s place and x is a thousand places.
So the second digit from the right hand side is the digit of the ten’s place in any number.
Now we have to find out the numbers in which ten’s place is filled by an even digit.
As we know, even digits are always divisible by 2.
So after checking out the numbers there are 7 numbers whose ten’s digit is filled by the even digit and which are given as
180, 127, 143, 122, 222, 162, 182.
Rest of them do not have an even digit on the ten’s place.
So the favorable number of outcomes = 7
Now as we know that the probability (P) is the ratio of the favorable number of outcomes to the total number of outcomes so we have,
$ \Rightarrow P = \dfrac{{{\text{favorable number of outcomes}}}}{{{\text{total number of outcomes}}}}$
$ \Rightarrow P = \dfrac{7}{{20}}$
So this is the required probability.
Hence option (C) is the correct answer.

Note – Whenever we face such types of question the key concept we have to remember is that always recall that the probability is the ratio of the favorable number of outcomes to the total number of outcomes, so first calculate these outcomes as above then put these outcomes in the formula of the probability and simplify, we will get the required probability.