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# Probability clarification

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Director
Joined: 07 Jun 2004
Posts: 610

Kudos [?]: 953 [1], given: 22

Location: PA

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31 Aug 2010, 11:34
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I have a fundamental Q to clarify based on the below problem

a deck of cards has 2 cards of blue , green , orange , red total 8 cards

what is the Probability of drawing two cards that are NOT blue

6/8 * 5/7 = 15/28

My Q is why cant we use the negation logic to get the same answer

that is 1 - ( both blue cards )

1 - 2/8 * 1/7 = 27 /28 why is this wrong ?

thanks
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Kudos [?]: 953 [1], given: 22

GMAT Tutor
Joined: 24 Jun 2008
Posts: 1344

Kudos [?]: 2010 [1], given: 6

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31 Aug 2010, 14:01
1
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Expert's post
rxs0005 wrote:
a deck of cards has 2 cards of blue , green , orange , red total 8 cards

what is the Probability of drawing two cards that are NOT blue

6/8 * 5/7 = 15/28

My Q is why cant we use the negation logic to get the same answer

that is 1 - ( both blue cards )

1 - 2/8 * 1/7 = 27 /28 why is this wrong ?

Both answers are correct, but they're answers to different questions. 15/28 is the probability that *neither* card is blue. 27/28, on the other hand, is the probability that the cards are not *both* blue. The second answer is much larger than the first, because it includes all of the ways in which you might pick one blue card and one non-blue card.
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Kudos [?]: 2010 [1], given: 6

Manager
Joined: 17 Mar 2010
Posts: 171

Kudos [?]: 211 [0], given: 9

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01 Sep 2010, 00:48

Kudos [?]: 211 [0], given: 9

Manager
Joined: 30 Aug 2010
Posts: 91

Kudos [?]: 197 [1], given: 27

Location: Bangalore, India

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01 Sep 2010, 04:36
1
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Negation logic can be used as shown below

Required P = 1 - (P of atlease 1 blue) = 1 - (P of 1 blue AND 1 another color OR 2 blue)

= 1- [( (2C1 * 6C1) + 2C2 )/8C2) = 1 - 13/28 = 15/28

Hope it helps.

Kudos [?]: 197 [1], given: 27

Re: Probability clarification   [#permalink] 01 Sep 2010, 04:36
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