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) $\dfrac{1}{3}$

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.

Total outcomes $=15+20+25$
Total outcomes $=60$ .
\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 $\dfrac{2}{3}$.