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# A magician has 5 animals in this magic hat: 3 doves and 2

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A magician has 5 animals in this magic hat: 3 doves and 2 [#permalink]  07 Oct 2012, 22:38
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A magician has 5 animals in this magic hat: 3 doves and 2 rabbits. If he pulls two animals out of the hat at random, which is the chance that he will have a matched pair.

[Reveal] Spoiler:

P( D 1st time) and P (D 2nd time) = 3/5 x 2/4 = 3/10
or
P (R 1st time) and P (R 2nd time) 1/5 x 1/4 = 1/20

3/10 + 1/20 = 7/20

However this is wrong

Thank you!

Last edited by Bunuel on 08 Oct 2012, 01:29, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Probability + Combinatorics: very confusing [#permalink]  07 Oct 2012, 23:40
chibimoon wrote:
Hi all
Q. A magician has 5 animals in this magic hat: 3 doves and 2 rabbits. If he pulls two animals out of the hat at random, which is the chance that he will have a matched pair.

P( D 1st time) and P (D 2nd time) = 3/5 x 2/4 = 3/10
or
P (R 1st time) and P (R 2nd time) 1/5 x 1/4 = 1/20

3/10 + 1/20 = 7/20

However this is wrong

Thank you!

You've worked out the probability for doves correctly. Although for the rabbits, it should be 2/5 x 1/4 = 1/10

So we would get 3/10 + 1/10 = 4/10 = 40%
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Re: Probability + Combinatorics: very confusing [#permalink]  07 Oct 2012, 23:42
Thank you so much, that was just a very embarrassing mistake
Re: Probability + Combinatorics: very confusing   [#permalink] 07 Oct 2012, 23:42
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