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# Draw 2 cards from a deck of cards minus Jokers. What's the

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Intern
Joined: 28 Aug 2004
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Draw 2 cards from a deck of cards minus Jokers. What's the [#permalink]  28 Aug 2004, 10:26
Draw 2 cards from a deck of cards minus Jokers.
What's the probability that a card is diamonds or hearts and a card is a queen?
Intern
Joined: 28 Aug 2004
Posts: 5
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Kudos [?]: 0 [0], given: 0

I don't know what the right way to solve this problem would be, but I think that you need to account for different scenarios of drawing queen first or drawing red first.

1. probability of drawing queen first:

red queen, red:
2/52 * 25/51

queen not red, red
2/52 * 26/51

50/2652 + 52/2652
= 102/2652

2. probability of drawing red first:

red not queen, queen:
24/52 * 4/51

red not queen, red queen:
24/52 * 2/51

96/2652 + 48/2652
= 144/2652

combining the two:
(102 + 144)/2652
= 123/1326
= 41/442

If the two scenarios have equal probabilities, though, then you can just double one of them:

2 (102/2652)
= 1/13

But no matter how much I scratch my head I can't figure out how they can be the same. could more knowledgeable folks comment on that?

j
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Joined: 07 Jul 2004
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Location: Singapore
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P(diamonds, exlcuding queen) = 12/52 + 3/52 - 1/52 = 7/26
P(hearts, exluding queen) = 7/26

P(diamonds or hearts) = 7/13
P(queen) = 4/52 = 1/13

So total = 8/13
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