Question

A number from $1-19$ is chosen at random. Find the probability of choosing an even number.
(a) $\dfrac{4}{19}$
(b) $\dfrac{9}{19}$
(c) $\dfrac{8}{19}$
(d) $\dfrac{11}{19}$

Answer 1

Hint: First of all, probability can be defined as uncertainty of an outcome. It can also be defined as ratio of number of possible outcomes of an event to occur to that of total number of possible outcomes of that event, which can be seen mathematically as, $\text{Probability=}\dfrac{\text{Number of possible outcomes}}{\text{Total number of outcomes}}$. So, first of all we will find the total number of outcomes and then from that we will find the number of outcomes for a number picked randomly from the list and it is an even number. Then by using the formula of probability we will find the answer.

Complete step by step answer:
In question we are given a list of numbers from $1-19$ and any one number is chosen from that list. We are asked to find the probability of the number chosen is an even number. So first of all, we will understand probability.
Probability can be defined as a measure of uncertainty of an outcome. In simple words we can say that it is an assumption of an event to occur. Probability of any event to occur ranges between 0 and 1. Now, the formula of probability can be given as,
$\text{Probability=}\dfrac{\text{Number of possible outcomes}}{\text{Total number of outcomes}}$
Now, to find the probability of the number chosen being an even number we will make a list of total outcomes and number of outcomes of an event to occur. So, list of total outcomes can be given as,
$\text{List of numbers}=\left\{ 1,2,3,4,5,6.......19 \right\}$
$\text{Total number of outcomes}=19$
Now, the list of even numbers can be given as,
$\text{List of even numbers}=\left\{ 2,4,6,8,10,12,14,16,18 \right\}$
So, $\text{Number of possible outcomes}=9$
Now, substituting these values in formula of probability we will get,
$\text{Probability}=\dfrac{\text{Number of possible outcomes}}{\text{Total number of outcomes}}=\dfrac{9}{19}$
Thus, the probability of the number chosen being an even number is $\dfrac{9}{19}$.
Hence, option (b) is the correct answer.

Note: Now, instead of finding the list of even numbers students can also find the list of odd number i.e. $\left\{ 1,3,5,7,9,11,13,15,17,19 \right\}$ and then find the probability of number being an odd number which can be given as, $\text{Probability}=\dfrac{\text{Number of possible outcomes}}{\text{Total number of outcomes}}=\dfrac{11}{19}$. Then to find the probability of even number, we have to subtract it from 1 as total probability of any event is maximum 1, so, $1-\dfrac{11}{19}=\dfrac{9}{19}$ as our final answer. In this way the answer does not change just the solution becomes quite long. So, this can be considered as an alternative method to solve the problem.