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

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Senior Manager
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In a bag of balloons, the ratio of red balloons to other [#permalink] New post 15 Oct 2008, 05:47
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In a bag of balloons, the ratio of red balloons to other colours is 1:5, if 3 balloons are selected from the bag at random, what is the probability that (a) at least one balloon is red, (b) exactly one balloon is red?
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Re: PSP004 [#permalink] New post 16 Oct 2008, 00:46
Probability of selecting a red baloon is 1/6 and probability of not selecting a red baloon = 5/6.

(a). Probability of at least 1 red baloon
= 1/6*5/6*5/6*3 + 1/6*1/6*5/6*3 + 1/6*1/6*1/6
= 91/216.

(b) Probability of exactly one red baloon
= 1/6*5/6*5/6*3 = 25/72.
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Re: PSP004 [#permalink] New post 16 Oct 2008, 10:01
scthakur wrote:
Probability of selecting a red baloon is 1/6 and probability of not selecting a red baloon = 5/6.

(a). Probability of at least 1 red baloon
= 1/6*5/6*5/6*3 + 1/6*1/6*5/6*3 + 1/6*1/6*1/6
= 91/216.

(b) Probability of exactly one red baloon
= 1/6*5/6*5/6*3 = 25/72.



i am getting 1/2 as answer
this is how I did it.

total sample space=6C3=20
red balloon can be selected in only 1 way , the other 2 balloons can be selected 5C2=10
so probability of selecting atleast one red balloon is 10/20=1/2

part B of the question is also the same in my opinion, i think it is just worded differently. since there is only one red balloon . the probability of selecting exactly one red balloon will also be the same i.e 1/2

vivek what is the OA
please also keep posting the OA so that we know whether our calculations are right or not.
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Re: PSP004 [#permalink] New post 17 Oct 2008, 00:36
ALD wrote:
scthakur wrote:
Probability of selecting a red baloon is 1/6 and probability of not selecting a red baloon = 5/6.

(a). Probability of at least 1 red baloon
= 1/6*5/6*5/6*3 + 1/6*1/6*5/6*3 + 1/6*1/6*1/6
= 91/216.

(b) Probability of exactly one red baloon
= 1/6*5/6*5/6*3 = 25/72.



i am getting 1/2 as answer
this is how I did it.

total sample space=6C3=20
red balloon can be selected in only 1 way , the other 2 balloons can be selected 5C2=10
so probability of selecting atleast one red balloon is 10/20=1/2

part B of the question is also the same in my opinion, i think it is just worded differently. since there is only one red balloon . the probability of selecting exactly one red balloon will also be the same i.e 1/2

vivek what is the OA
please also keep posting the OA so that we know whether our calculations are right or not.


Thakur is right OA are
a) Probability of at least 1 red baloon
= 1/6*5/6*5/6*3 + 1/6*1/6*5/6*3 + 1/6*1/6*1/6
= 91/216.

(b) Probability of exactly one red baloon
= 1/6*5/6*5/6*3 = 25/72.
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Re: PSP004 [#permalink] New post 18 Oct 2008, 23:17
guys
can someone pls tell me the green part?
(b) Probability of exactly one red baloon
= 1/6*5/6*5/6*3 = 25/72.

i get the 1/6 but not the follwing numbers?!
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Re: PSP004 [#permalink] New post 18 Oct 2008, 23:45
scthakur wrote:
Probability of selecting a red baloon is 1/6 and probability of not selecting a red baloon = 5/6.

(a). Probability of at least 1 red baloon
= 1/6*5/6*5/6*3 + 1/6*1/6*5/6*3 + 1/6*1/6*1/6
= 91/216.

(b) Probability of exactly one red baloon
= 1/6*5/6*5/6*3 = 25/72.


why are we multiplying 3 here ? Is the order necessary ?
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Re: PSP004 [#permalink] New post 19 Oct 2008, 21:04
amitdgr wrote:
scthakur wrote:
Probability of selecting a red baloon is 1/6 and probability of not selecting a red baloon = 5/6.

(a). Probability of at least 1 red baloon
= 1/6*5/6*5/6*3 + 1/6*1/6*5/6*3 + 1/6*1/6*1/6
= 91/216.

(b) Probability of exactly one red baloon
= 1/6*5/6*5/6*3 = 25/72.


why are we multiplying 3 here ? Is the order necessary ?


Yes. The question says "at least one baloon is read"....this means it could be the first baloon, second or the third baloon.
Re: PSP004   [#permalink] 19 Oct 2008, 21:04
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