Probability

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eskander: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Sat Mar 24, 2012 3:26 am

Probability

by eskander » Sat May 19, 2012 2:06 pm

Could you please help me out. I must be missing some step in calculations...

There are 10 bottles wine in a carton. Three bottles will be selected and examined at random. If any of the three bottles is defective, the carton will be sent back. If a carton contains exactly three defective bottles, what is the probability that the carton will not be sent back?
(A) 1/9
(B) 3/10
(C) 7/10
(D) 7/24
(E) 17/24

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Source: Beat The GMAT — Problem Solving | Sat May 19, 2012 2:06 pm

coolhabhi: Master | Next Rank: 500 Posts; Posts: 141; Joined: Tue Oct 04, 2011 5:17 am; Thanked: 25 times

by coolhabhi » Sat May 19, 2012 2:26 pm

IMO : D

there are exactly three defective bottles and 7 non defective bottles.

So if the three bottles are picked up from the 7 non defective bottles then the case will not be sent back.

=>probability of choosing 1st non defective bottle = 7/10
=>probability of choosing 2nd non defective bottle = 6/9
=>probability of choosing 3rd non defective bottle = 5/8

=> (7*6*5)/(10*9*8)
=> 7/24

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ihatemaths: Master | Next Rank: 500 Posts; Posts: 122; Joined: Tue May 01, 2012 6:05 am; Thanked: 3 times

by ihatemaths » Sun May 20, 2012 5:17 am

defective->3
non-defe->7
total->10

condition for returning back is atleast one i.e if even 3c1 package is sent back

condition ensuring non-return is : (7c3 * 3c0)/10c3 = 7/24

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Yermek1984: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Sun May 20, 2012 5:47 am

by Yermek1984 » Sun May 20, 2012 7:07 am

coolhabhi, I must disagree with u. May be I was wrong on this, but here is my option:
1) the probability of choosing at least 1 defective bottle = (3*7*6)/(10*9*8)= 7/40;
2) the probability of choosing at least 2 defective bottles = (3*2*7)/(10*9*8) = 7/120;
3) the probability of choosing at least 3 defective bottles = (3*2*1)/(10*9*8) = 1/120;

Since, we have to figure out the probability when a cartoon won't sent back, then the P. = (1-(7/40+7/120+1/120)) = 91/120;

I'm not sure, but there are no correct answers. Correct me plz if I'm not right.

Yermek