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# In a bag of balloons, the ratio of red balloons to other is

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CEO
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In a bag of balloons, the ratio of red balloons to other is [#permalink]  01 Oct 2003, 13:27
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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
Intern
Joined: 29 Aug 2003
Posts: 49
Location: Detroit, MI
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Re: PS : Probability ..Balloons [#permalink]  02 Oct 2003, 06:23
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
Eternal Intern
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yeah [#permalink]  02 Oct 2003, 06:38
take a FINITE MATH Course it will help on probablity i learned this in class.
Eternal Intern
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yeah [#permalink]  02 Oct 2003, 06:39
take a FINITE MATH Course it will help on probablity i learned this in class.
Consultant
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PS : Probability ..Balloons [#permalink]  02 Oct 2003, 06:41
Dear All,

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
Intern
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Re: PS : Probability ..Balloons [#permalink]  02 Oct 2003, 06:54
Hakob wrote:
Dear All,

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.

Hope that makes it clear.
CEO
Joined: 15 Aug 2003
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Kudos [?]: 703 [0], given: 781

Re: PS : Probability ..Balloons [#permalink]  02 Oct 2003, 11:24
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
CEO
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[#permalink]  12 Oct 2003, 04:14
Amar,

A question
Did we assume in the above that we replace the balloons?
Can we assume replacement if not given in the problem?

Thanks
Praetorian
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[#permalink]  12 Oct 2003, 18:35
Yes,

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.

Amar.
[#permalink] 12 Oct 2003, 18:35
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# In a bag of balloons, the ratio of red balloons to other is

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