Question

A number from 1 to 11 is chosen at random. What is the probability of choosing an odd number?
A. $\dfrac{1}{{11}}$
B. $\dfrac{5}{{11}}$
C. $\dfrac{6}{{11}}$
D. None of these

Answer 1

Hint:
In the solution, a number is randomly drawn from 1 to 11. We ought to calculate the probability of having an odd number. First we have to calculate the total number of outcomes from the given sample. After that we have to calculate the total odd number present in the sample. Finally we have to divide that value with the total number of outcomes.

Complete step by step solution:
It is given a number from 1 to 11 is chosen at random and we have to find the probability of choosing an odd number.
The numbers from 1 to 11 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.
Thus, total numbers from 1 to 11 = 11
Odd numbers present in the given sample are 1, 3, 5, 7, 9 and 11
Thus, total odd numbers from 1 to 11 = 6
Now we have to find the probability of choosing an odd number for which we have to divide the total odd numbers present in between 1 to 11 that is 6 by total numbers from 1 to 11 which is 11.
Thus the probability of choosing an odd number is
$\begin{array}{l} \Rightarrow P\left( {{\rm{an}}\;{\rm{odd}}\;{\rm{number}}} \right) = \dfrac{{{\rm{total}}\;{\rm{odd}}\;{\rm{number}}}}{{{\rm{total}}\;{\rm{number}}}}\\ \Rightarrow P\left( {{\rm{an}}\;{\rm{odd}}\;{\rm{number}}} \right) = \dfrac{6}{{11}}\end{array}$
Hence, the required probability is $\dfrac{6}{{11}}$.

Note:
Probability explains the chances of happening in an event. Here we have to determine the probability of choosing an odd number for the given data. Since the total number of samples and the total odd numbers present in the data can be calculated, thus it is easy to find out the probability of choosing an odd number.