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Probability test (Posted on 2005-03-03) Difficulty: 2 of 5
Five cards are drawn from a pack of 52 cards. What is the probability that exactly three of them are of the same suit.

See The Solution Submitted by Sandeep    
Rating: 3.0000 (3 votes)

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re: Solution? | Comment 6 of 13 |
(In reply to Solution? by jduval)

Here is were you are missing some probabilty;

The first 4 cards can be two doulbe suits, in wich case the fith card has 22/48.

Thre first 4 cards already have 3 of the same suit, in wich case the fith card has 38/48.

So the last cards probability is somewhere betwenn 11/48 and 38/48, with a naive average (~25/48) we get about twice the probability you originally got and the correct answer (1/3).

But your logic does give a lower limit (we know that the probabilty is higher than 1/6).
  Posted by ajosin on 2005-03-03 15:53:59

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