Question

A Bag contains $5$ white, $7$ red and $3$ black balls. If a ball is chosen at random, then find the probability that it is not red.

Answer 1

Hint: To solve this question, we will start with finding the total number of balls in the bag, then we will take the favourable outcomes of getting red balls, then after applying the values in the probability formula we will get the probability of getting a red ball. Now to get the probability of not getting a red ball, we will subtract the probability of getting a red ball from \[1,\] because \[1\] indicates certainty of the event, hence, we will get our required answer.

Complete step-by-step answer:
We have been given a bag that contains $5$ white, $7$ red and \[3\] black balls. It is given that a ball is chosen at random, we need to find the probability that it is not red.
So, total number of outcomes of balls \[ = {\text{ }}5{\text{ }} + {\text{ }}7{\text{ }} + {\text{ }}3{\text{ }} = {\text{ }}15\]
And the number of favourable outcomes of getting red balls \[ = {\text{ }}7\]
We know that, Probability $ = \dfrac{{{\text{favourable outcomes}}}}{{{\text{total outcomes}}}}$
On applying the values in the above formula, we get
Probability of getting a red ball \[ = \dfrac{7}{{15}}\]
Probability of not getting a red ball \[ = {\text{ }}1{\text{ }} - \] probability of getting a red ball.
$ = 1 - \dfrac{7}{{15}}$
$ = \dfrac{8}{{15}}$
Thus, probability of not getting a red ball is \[\dfrac{8}{{15}}.\]

Note: To solve the above question, there is an alternate method of finding the probability of not getting a red ball.
Probability of not getting a red ball \[ = \] Probability of getting white and black balls.
Number of favourable outcomes of getting white and black balls \[ = {\text{ }}5{\text{ }} + {\text{ }}3{\text{ }} = {\text{ }}8\]
Probability of not getting a red ball \[ = \] Probability of getting white and black balls $ = \dfrac{8}{{15}}$