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, a blue balloon

#### Solution 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

Let B be the event of getting a blue balloon.

Given: n(B) = 3

`therefore "P"("B") = ("n"("B"))/("n"("S"))`

= `3/9`

= `1/3`

Hence, the probability of the event that Pranali gets a blue baloon is `1/3.`

#### Solution 2

Let the 2 red balloons be R_{1}, R_{2}, 3 blue balloons be B_{1}, B_{2}, B_{3} and 4 green balloons be G_{1}, G_{2}, G_{3}, G_{4}.

∴ Sample space,

S = {R_{1}, R_{2}, B_{1}, B_{2}, B_{3}, G_{1}, G_{2}, G_{3}, G_{4}}

∴ n(S) = 9

Let B be the event that Pranali gets a blue balloon

∴ B = {B_{1}, B_{2}, B_{3}}

∴ n(B) = 3

∴ P(B) = `("n"("B"))/("n"("S"))`

= `3/9`

∴ P(B) = `1/3`