Question & Answer
QUESTION

A bag contains 15 cabbages, 20 carrots, and 25 turnips. If a single vegetable is picked at random from the bag, what is the probability that it will not be a carrot?
A) \[\dfrac{2}{3},\ .666\ or\ .667\]
B) \[\dfrac{2}{4}\]
C) \[\dfrac{3}{4}\]
D) \[\dfrac{1}{3}\]

ANSWER Verified Verified
Hint: In the question, the ‘not’ means that the probability of that event not taking place is to be found.
The formula for evaluating probability of any event is
P \[=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}\] .
Another important thing which is useful for this question is that picking a vegetable from the bag at random is nothing but taking out a vegetable without having any bias towards any vegetable and without having any prior information regarding the vegetables.

Complete step-by-step answer:
Now, in the question it is mentioned that there are 15 cabbages, 20 carrots, and 25 turnips in the bag.
So, the total outcomes for the event of drawing a vegetable at random from the bag is
Total outcomes \[=15+20+25\]
Total outcomes \[=60\] .
Now, for favorable outcomes for not getting a carrot, we need to count the total number of vegetables that are there other than carrot which is as follows
Favorable outcomes
 \[\begin{align}
  & =15+25 \\
 & =40 \\
\end{align}\]
Now, using the formula for calculating the probability of getting a white ball from the bag \[\begin{align}
  & =\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}} \\
 & =\dfrac{40}{60} \\
 & =\dfrac{2}{3} \\
\end{align}\]
Hence, the probability of not getting a carrot from the bag is \[\dfrac{2}{3}\].

Note: Another way of doing this question is that the probability of getting a carrot is not asked, so, we can subtract the probability (of getting a carrot from the bag) from 1 and through this method, we will also get the correct answer.