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# A deck of cards contains 2 blue cards, 2 orange cards, 2

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A deck of cards contains 2 blue cards, 2 orange cards, 2 [#permalink]  22 Jan 2006, 08:00
A deck of cards contains 2 blue cards, 2 orange cards, 2 yellow cards, and 2 black cards. If two cards are randomly drawn, what is the probability that they will both not be black?
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Re: probability question [#permalink]  22 Jan 2006, 08:25
=1-[(2/8)(1/7)=(56-2)/56=27/28
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(6C2)/(8C2)
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21stCenturion wrote:
(6C2)/(8C2)

nope, that excludes the chances to have a black card with any other color card.
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21stCenturion wrote:

(6C2)/(8C2)
this means none of the two cards will be black.
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Yes, that makes sense.. Thanks.
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Re: probability question [#permalink]  22 Jan 2006, 10:02
Professor wrote:
=1-[(2/8)(1/7)=(56-2)/56=27/28

I got 55/56
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2/8 is the number of ways of selecting the first card that is black.

Hope this clarifies.
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1-(2/8*1/7) = 27/28.
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Both Not black = 1 - Both black
= 1 - (2/8 * 1/7) = 27/28
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Total now of ways in which you can draw 2 cards from 8 cards = 8C2 = 28 ways.

P(Both not black) = 1 - P(Both black)

n(both black) = 2C2 = 1.

Therefore ans = 1-(1/28) = 27/28
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21stCenturion wrote:
2/8 is the number of ways of selecting the first card that is black.

Hope this clarifies.

Thanks ))My fault I was thinking it should be 1/8.Now I see where i was wrong
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im confused as to why you mulitply 2/8 by 1/7. Where does the 1/7 come from?

Also where does the 56-2 come from? Dont you get 2/56 after multiplying? Not sure why we subtract 2 from 56 then divide by 56.

THANKS!!
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hedder02 wrote:
im confused as to why you mulitply 2/8 by 1/7. Where does the 1/7 come from?

Also where does the 56-2 come from? Dont you get 2/56 after multiplying? Not sure why we subtract 2 from 56 then divide by 56.

THANKS!!

Let me explain.

Probability of both NOT black = 1- Probability of both black

Meaning of two cards taken at random means take them one by one without replacement.

At the time of taking first card:
Probability that this card is black = # of black cards/total cards = 2/8
Now we have 7 cards and first card taken out was black. So 1 more black card is left.

At the time of taking second card:

Probability that this card is black = # of remaining black cards/total cards = 1/7

Prob that both are black = 2/8 * 1/7 = 2/56 = 1/28

Probability of both NOT black = 1- Probability of both black
Probability of both NOT black = 1- 1/28 = 27/28

Hope this helps.
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its 27/28

1- P(1st Black)*P(2nd Black)
1- 2/8 * 1/7 (because its a random draw)
=27/28
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P(not both black) = 1-P(both are black) = 1-(2/8 * 1/7) = 1-(1/28) = 27/28
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Try changing the question to "draw both cards at the same time" (Not one after another)
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