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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

please explain - why do you think that the bag contains 6 balls. The problems states "the ratio of red to other"!!! it can be 1:5, 2:10 etc

maybe I am missing smth?

Good luck, Hakob

Hakob,

The ratio is given as 1:5. The multiples given by you, of that ratio are also right. If the ratio is 1:5, it means that there is 1 red ball for 5 balls of other kinds.

Say there are n balls in all.
Number of red balls = r
Number of other balls = o

r + o = n
and r/o = 1/5 => o=5*r

So, 6*r = n => r = n/6 which means that the number of red balls equals a sixth of the total number of balls.

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

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

I did assume that. I wouldn't expect the actual GMAT questions to be ambiguous like this one. If they were, I would go with both the approaches (replaced and not replaced) and try to see which one yileds a solution. If both are present, then we are at a loss.