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Probability clarification

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Probability clarification [#permalink] New post 31 Aug 2010, 10:34
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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


The answer is

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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Re: Probability clarification [#permalink] New post 31 Aug 2010, 13:01
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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

The answer is

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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Re: Probability clarification [#permalink] New post 31 Aug 2010, 23:48
Nice question and amazing answer
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Re: Probability clarification [#permalink] New post 01 Sep 2010, 03:36
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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.
Re: Probability clarification   [#permalink] 01 Sep 2010, 03:36
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