Question

Choose the correct option for the following problem,
There are $2$ red balls and $3$ blue balls and $5$ green balls in a bag. If a ball is drawn at a time, find the probability that it is not a red ball.
A. $\dfrac{2}{5}$
B. $\dfrac{7}{4}$
C. $\dfrac{4}{5}$
D. $\dfrac{1}{5}$

Answer 1

For solving this particular problem we have to find the total number of outcomes and the favourable outcomes that is ,the drawn ball is not a red ball. Here eight is taken as a favourable outcome and ten as a total number of outcomes. By putting these values into the formula we will get the probability of the required event.

Complete step by step answer:
Number of red balls are $2$,the number of blue balls are $3$ , and the number of green balls are $5$. Therefore , total number of balls given by,
Number of red balls $+$ Number of blue balls $+$ Number of green balls
$\Rightarrow 2 + 3 + 5 \\\ \Rightarrow 10 \\\$
Now let A be an event that the drawn ball is red,
$P(A)= \dfrac{Favourable\,outcomes}{Total\,number\,of\,outcomes}$
Here , a favourable outcome is drawing a red ball and the total number of outcomes are ten.Therefore,
p(A) = \dfrac{2}{{10}} \\\ \Rightarrow p(A) = \dfrac{1}{5} \\\
We have to find the probability that it is not a red ball,
Let B be an event that the drawn ball is not red , that is one minus the probability of drawing a red ball,
$p(B) = 1 - p(A)$
$p(B) = 1 - \dfrac{1}{5} \\\ \Rightarrow p(B) = \dfrac{4}{5} \\\$
Therefore, the probability of drawing not a red ball is $\dfrac{4}{5}$.

Therefore , the option C is correct.

Note: The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory, which is also used in the probability distribution, where you will learn the possibility of outcomes for a random experiment. To find the probability of a single event to occur, first, we should know the total number of possible outcomes.