amarsesh wrote:

praetorian123 wrote:

In a bag of balloons, the ratio of red balloons to other is 1:5

if 3 Balloons are selected at random, what is the probability that

1. at least one balloon is red

2. exactly one balloon is red

The probability of getting a red balloon = 1/6

(2)Prob. that exactly exactly one balloon is red

The first balloon can be red or the second one or the third one

= 3 * (1/6)((5/6)^2) = 25/72 or 75/216

(1) Probabilti that atleast one balloon is red = Prob. that only 1 balloon is red + Prob. that only 2 balloons are red + Prob. that all 3 balloons are red

= 75/216 + (3 * ((1/6)^2) * (5/6)) + (1/6)^3 = 91/216

Good work..Amar.

Just a simpler way

1. Probability that atleast one balloon is red = 1 - Prob none are red

prob that a balloon is red = 1/6

so prob that its not red = 5/6

Prob none of the three are red = (5/6)^ 3 =125/216

So required prob = 1- 125/216 = 91/216

2. Prob that exactly one is red

we can get exactly one in any of the three ways

R O O

O R O

O O R

so it follows

1/6 * 5/6 * 5/6 * 3 = 75/216