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# What is the probability of getting two cards belonging to

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Intern
Joined: 13 Aug 2005
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What is the probability of getting two cards belonging to [#permalink]

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28 Aug 2005, 15:14
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What is the probability of getting two cards belonging to two different suits when two cards are drawn at random from a pack of well shuffled cards comprising 52 cards?

a. 1/13
b. 13/17
c. 13/51
d. 26/51
e. 12/51

Can you explain this one?
Thanks, Yaron
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28 Aug 2005, 17:09
hmm..i cant seem to get it. here's my working

Prob of drawing one card of a suit = 13/52 = 1/4
Prob of drawing second card of one of the 3 OTHER suits = 13*3/51(51 since one card has already been drawn). = 13/17

So i get (1/4)*(13/17) = 13/68 which of course isnt in the answers. so where did i go wrong?
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28 Aug 2005, 17:29
I think it is B:

what card we get first doesn't matter, what matters is the second one. If we count the probability of getting the second card different from the first card we get the answer:

as we already took one card the total number is 51, and we have 39 cards that are different from the one that was taken first. So, the probability of getting a card different from the first is 39/51, or 13/17
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28 Aug 2005, 18:37
ahh yes i see my mistake now. first card is actually anything since suit doesnt matter...cheers suslik!
28 Aug 2005, 18:37
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