Question

A bag contains yellow and black balls. The probability of getting a yellow ball from the bag is $ \dfrac{1}{3} $ .
What is the probability of not getting a yellow ball?
A. $ \dfrac{1}{3} $
B. $ \dfrac{2}{3} $
C. $ \dfrac{5}{3} $
D. $ \dfrac{7}{3} $

Answer 1

Hint: 1.In such types of questions it is important for the students to understand the probability terms given.
2. In this question students need to classify the data as the events mentioned and total outcomes.
3.The tricky part in this is to establish the relationship between the events and the outcomes.
It is the number of results obtained divided by the total number of outcomes.
If X is the event then
 $ P(X) = $ Number of outcomes in an event\[/\] Total number of outcomes
 $ P(X) = P(YELLOW) + P(BLACK) $


Complete step-by-step answer:
Let us understand what the question says.
It says that there is a bag of balls in which there are two types of balls.
One is yellow balls and another is black balls.
We have been provided with the information that the probability that the ball picked from the ball of bags is $ \dfrac{1}{3} $ .
let us put it this way ,
 $ P(YELLOW) = \dfrac{1}{3} $
We have been asked the probability that the ball is not yellow.
In other words the probability that the ball is black.
As a sum $ $ the probability is always 1.
That is,
If X is the Probability which carries the unit value 1.
Then,
 $ \Rightarrow P(X) = P(YELLOW) + P(BLACK) $
 $ P(X) = 1 $
 $ \Rightarrow P(BLACK) = P(X) - P(YELLOW) $
 $ \Rightarrow P(BLACK) = 1 - \dfrac{1}{3} $
 $ \Rightarrow P(NOT YELLOW) = \dfrac{2}{3} $
Thus, the probability that the ball is not yellow is $ \dfrac{1}{3} $

So, the correct answer is “Option A”.

Note: Students must understand what is asked in such a question and should be able to classify the data correctly.
Students might mess up while putting the values in the actual equation.