Question

A balloon vendor 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 Pranali gets,
(1) a red balloon
(2) a blue balloon
(3) a green balloon.

Answer 1

Given:
Number of red baloon = 2
Number of blue baloon = 3
Number of green baloon = 4
Let S be the sample space.
∴ n(S) = Number of red baloon + Number of blue balloon + Number of green balloon
= 2 + 3 + 4
= 9
(1) Let A be the event of getting a red balloon.
Given: n(A) = 2
$$\begin{gathered} \therefore \mathrm{P}\left(\mathrm{A}\right)=\frac{\mathrm{n}\left(\mathrm{A}\right)}{\mathrm{n}\left(\mathrm{S}\right)} \\ =\frac{2}{9} \end{gathered}$$
Hence, the probability of the event that Pranali gets a red baloon is $\frac{2}{9}$.
(2) Let B be the event of getting a blue balloon.
Given: n(B) = 3
$$\begin{gathered} \therefore \mathrm{P}\left(\mathrm{B}\right)=\frac{\mathrm{n}\left(\mathrm{B}\right)}{\mathrm{n}\left(\mathrm{S}\right)} \\ =\frac{3}{9} \\ =\frac{1}{3} \end{gathered}$$
Hence, the probability of the event that Pranali gets a blue baloon is $\frac{1}{3}$.
(3)
Let C be the event of getting a green balloon.
Given: n(C) = 4
$$\begin{gathered} \therefore \mathrm{P}\left(\mathrm{C}\right)=\frac{\mathrm{n}\left(\mathrm{C}\right)}{\mathrm{n}\left(\mathrm{S}\right)} \\ =\frac{4}{9} \end{gathered}$$
Hence, the probability of the event that Pranali gets a green baloon is $\frac{4}{9}$.