Question

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 a red or blue ball.
A. $\dfrac{1}{2}$
B. $\dfrac{7}{10}$
C. $\dfrac{8}{10}$
D. $\dfrac{1}{10}$

Answer 1

Hint : For this type of probability problems when two balls are required to be drawn one by one, to find total probability we first calculate their individual probability and then add them to find total probability of the asked event.
Formulas used: Probability of any event E is defined as:
$P(E) = \dfrac{{number\,\,of\,\,favourable\,\,outcome}}{{total\,\,number\,\,of\,\,possible\,\,outcomes\,\,of\,event}}$

Complete step-by-step answer :
Here, in the given problem there are $2$ red balls, $3$ blue balls and $5$ green balls in bags.
Total number of balls in the bag is equal to the sum of all balls.
Therefore, total number of balls in bag is given as: $2 + 3 + 5$
Total number of balls $= 10$
To find the probability of a red or blue ball. We first calculate the probability of getting a red ball.
Number of red balls in favor = 2
Total numbers of balls in bag = $10$
Therefore, probability of red ball is = $\dfrac{{number\,\,of\,\,red\,\,balls\,\,in\,\,bag}}{{total\,\,numbers\,\,of\,\,balls\,\,in\,\,bag}}$
$= \dfrac{2}{{10}} = \dfrac{1}{5}$
Hence, the probability of drawing a red ball from a bag is $\dfrac{1}{5}$ .
Now, we find the probability of getting a blue ball from the bag.
Number of blue ball in bag = $3$
Total numbers of ball in bag = $10$
Therefore, probability of blue ball is = $\dfrac{{number\,\,of\,\,blue\,\,balls\,\,in\,\,bag}}{{total\,\,numbers\,\,of\,\,balls\,\,in\,\,bag}}$
$= \dfrac{3}{{10}}$
Hence, the probability of drawing a blue ball from a bag is $\dfrac{3}{{10}}$ .
Therefore, to find the probability of drawing a red or blue ball from a bag can be obtained by adding two probabilities calculated above.
$\Rightarrow$ $\text{ Probability of red or blue ball}= \dfrac{1}{5} + \dfrac{3}{{10}} = \dfrac{{2 + 3}}{{10}} = \dfrac{5}{{10}} = \dfrac{1}{2}$
Therefore, from above we see that the probability of drawing a red or blue ball from a bag is $\dfrac{1}{2}.$
So, the correct answer is “Option A”.

Note : In probability problems if events are independent then the probability of event can also be calculated by finding direct sum of events and then dividing it by total numbers of sample space instead of calculating them as individuals and then adding them to obtain required probability.