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A shipment of 8 television sets contains 2 black-and-white

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Manager
Joined: 25 Apr 2007
Posts: 50
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A shipment of 8 television sets contains 2 black-and-white [#permalink]  24 Oct 2007, 14:02
A shipment of 8 television sets contains 2 black-and-white sets and 6color sets. If 2 television sets are to be chosen at random from this shipment, what is the probability that at least 1 of the 2 sets chosen will be a black-and-white set?

A. 1/7 B. ¼ C. 5/14 D. 11/28 E. 13/26

The way i tried to solve this is - it says atleast 1 B&W so you can calculate prob for getting 1 B&W and 2 B&W.

2/8 * 6/7 + 2/8 * 1/7 = 1/4 but the answer key says E.

Cheers !!
Senior Manager
Joined: 04 Jan 2006
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Re: Probability Set 24-Q 4 [#permalink]  24 Oct 2007, 14:10
johnbaker wrote:
A shipment of 8 television sets contains 2 black-and-white sets and 6color sets. If 2 television sets are to be chosen at random from this shipment, what is the probability that at least 1 of the 2 sets chosen will be a black-and-white set?

A. 1/7 B. ¼ C. 5/14 D. 11/28 E. 13/26

The way i tried to solve this is - it says atleast 1 B&W so you can calculate prob for getting 1 B&W and 2 B&W.

2/8 * 6/7 + 2/8 * 1/7 = 1/4 but the answer key says E.

Cheers !!

Prob[Blk&Whte >= 1] = 1 - Prob[No Blk&Whte Selected]
= 1 - (6/8)x(5/7)
= 1 - 15/28 = 13/28

Could you check Choice (E) whether it is 13/26 or 13/28?
Manager
Joined: 25 Apr 2007
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I checked and it says 13/26 which didn't make any sense. mayb that should have been 13/28.

Thanks.
Senior Manager
Joined: 04 Jan 2006
Posts: 280
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Re: Probability Set 24-Q 4 [#permalink]  24 Oct 2007, 14:14
johnbaker wrote:
A shipment of 8 television sets contains 2 black-and-white sets and 6color sets. If 2 television sets are to be chosen at random from this shipment, what is the probability that at least 1 of the 2 sets chosen will be a black-and-white set?

A. 1/7 B. ¼ C. 5/14 D. 11/28 E. 13/26

The way i tried to solve this is - it says atleast 1 B&W so you can calculate prob for getting 1 B&W and 2 B&W.

2/8 * 6/7 + 2/8 * 1/7 = 1/4 but the answer key says E.

Cheers !!

I believe you miss something in your calculation.

Prob[B&W >= 1] = Prob[B and W] + Prob[B and B]
= (2C1)x(2/8)x(6/7) + (2/8)x(1/7)
= 3/7 + 2/56 = (24+2)/56 = 13/28

You miss (2C1) in your calculation.
Director
Joined: 11 Jun 2007
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i recently posted this question.. its a typo!
http://www.gmatclub.com/forum/t53338
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