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Probability Ques

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Intern
Joined: 30 Jun 2019
Posts: 46

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23 Nov 2019, 09:35
Hey Guys

What can be the quickest approach to this question:-

A bag contains 3 Blue 5 Green 4 yellow balls
3 balls are drawn at random without replacement. What is the probability that exactly 2 of the 3 balls will be Blue.?

The approach i used is very lengthy and I think not correct or advisable

I used 1-(Prob of All Blue + Prob of no Blue + Prob of One Green)

Thanks

Posted from my mobile device
Math Expert
Joined: 02 Aug 2009
Posts: 8310

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23 Nov 2019, 22:38
Sam10smart wrote:
Hey Guys

What can be the quickest approach to this question:-

A bag contains 3 Blue 5 Green 4 yellow balls
3 balls are drawn at random without replacement. What is the probability that exactly 2 of the 3 balls will be Blue.?

The approach i used is very lengthy and I think not correct or advisable

I used 1-(Prob of All Blue + Prob of no Blue + Prob of One Green)

Thanks

Posted from my mobile device

The correct way would be
Ways in which 2 are blue 3C2 and the third could be any of 5+4 or 9..3C2*9C1=3*9=27
Total ways = (3+5+4)C3=12C3=12*11*10/3*2=220

Prob=27/220
_________________
Intern
Joined: 30 Jun 2019
Posts: 46

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23 Nov 2019, 22:56
chetan2u wrote:
Sam10smart wrote:
Hey Guys

What can be the quickest approach to this question:-

A bag contains 3 Blue 5 Green 4 yellow balls
3 balls are drawn at random without replacement. What is the probability that exactly 2 of the 3 balls will be Blue.?

The approach i used is very lengthy and I think not correct or advisable

I used 1-(Prob of All Blue + Prob of no Blue + Prob of One Green)

Thanks

Posted from my mobile device

The correct way would be
Ways in which 2 are blue 3C2 and the third could be any of 5+4 or 9..3C2*9C1=3*9=27
Total ways = (3+5+4)C3=12C3=12*11*10/3*2=220

Prob=27/220

Dear Sir

Thank you so much.

Can you also try and get the same result using my approach?

Thanks
Math Expert
Joined: 02 Aug 2009
Posts: 8310

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23 Nov 2019, 23:11
Sam10smart wrote:
chetan2u wrote:
Sam10smart wrote:
Hey Guys

What can be the quickest approach to this question:-

A bag contains 3 Blue 5 Green 4 yellow balls
3 balls are drawn at random without replacement. What is the probability that exactly 2 of the 3 balls will be Blue.?

The approach i used is very lengthy and I think not correct or advisable

I used 1-(Prob of All Blue + Prob of no Blue + Prob of One Green)

Thanks

Posted from my mobile device

The correct way would be
Ways in which 2 are blue 3C2 and the third could be any of 5+4 or 9..3C2*9C1=3*9=27
Total ways = (3+5+4)C3=12C3=12*11*10/3*2=220

Prob=27/220

Dear Sir

Thank you so much.

Can you also try and get the same result using my approach?

Thanks

So probability of all blue =3C3/12C3=1/220
Probability of one blue = 3C1*9C2/12C3=3*36/220=108/220
Probability of none blue =9C3/12C3=84/220
Total ways =1-(1/220+108/220+84/220)=1-(1+108+84)/220=1-193/220=27/220
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Intern
Joined: 30 Jun 2019
Posts: 46

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23 Nov 2019, 23:30
chetan2u thanks alot!!

Posted from my mobile device
Re: Probability Ques   [#permalink] 23 Nov 2019, 23:30
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