Question

A balloon vender has 2 red, 3 blue and 4 green balloons. He wants to choose one of them at random to give it to Pranali. What is the probability of the event that
(i) A red balloon
(ii) a blue balloon
(iii) a green balloon.

Answer 1

Hint: To solve this question first we need to calculate the total number of balloons a balloon vendor has and then we calculate the number of favorable outcomes. Then, by using the formula of probability, we get our desired solution.
 Following formula is used-
 $ P\left( A \right)=\dfrac{n\left( E \right)}{n\left( S \right)} $
Where, A is an event,
\[n\left( E \right)=\] Number of favorable outcomes and $ n\left( S \right)= $ number of total possible outcomes

Complete step-by-step answer:
We have given that a balloon vendor has 2 red, 3 blue and 4 green balloons, so the total number of balloons he has is $ =2+3+4=9 $ .
So, we have $ n\left( S \right)=9 $
Now, we have given that he wants to choose one of them at random to give it to Pranali.
We have to find the probability of the event being a red balloon, a green balloon, a blue balloon.
Now, we start with the part (i)
(i) A red balloon
As we have given that a balloon vendor has 2 red balloons and he has to choose one balloon from total 9 balloons. So, the probability that Pranali get the red balloon will be
 $ P\left( A \right)=\dfrac{n\left( E \right)}{n\left( S \right)} $
We have 2 favorable outcomes, so the probability will be
 $ P\left( R \right)=\dfrac{2}{9} $
Now, let’s take part (ii)
(ii) a blue balloon
As we have given that a balloon vendor has 3 blue balloons and he has to choose one balloon from total 9 balloons. So, the probability that Pranali get the blue balloon will be with 3 favorable outcomes
 $ P\left( B \right)=\dfrac{3}{9} $
Now, we solve part (iii)
(iii) a green balloon
As we have given that a balloon vendor has 4 green balloons and he has to choose one balloon from total 9 balloons. So, the probability that Pranali get the green balloon will be with 4 favorable outcomes
 $ P\left( G \right)=\dfrac{4}{9} $
So, we have the probability of the events that a red balloon, a blue balloon and a green balloon are $ \dfrac{2}{9},\dfrac{3}{9} $ and $ \dfrac{4}{9} $ respectively.

Note: As given three events are independent to each other, so no need to combine all to get the answer. We have to calculate each case individually. Also, when we calculate the probability of occurrence of any event the value should lie between 0-1. The value of probability cannot exceed one. Probability value higher than one means probability greater than $ 100% $ and it is not possible.