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From an ordinary deck of cards, only 12 picture cards are [#permalink]
13 Oct 2004, 16:45

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(i) From an ordinary deck of cards, only 12 picture cards are retained. They are shuffled (mixed) and a man draws 2 cards at random. He then announce one of these cards is the King or Spades. What is the probability that he holds two Kings? (hint: list the possible sample space carefully).

(ii) The 2 cards are replaced and the cards re-shuffled. He then draws 2 cards, and announces that he holds at least one King. Find the probability that he holds two Kings in his hand.

you did not consider that he has announced that he got a king.

[quote="Anonymous"]1. There are 4 kings in a pack of cards. If we need to select 2 out of the 4, we can do it in 4C2 ways. The prob is then 4C2/12C2 => 1/11.

2. Atleast one king means the no. of ways would be: (4C1*8C1+4C2) [b]/ [/b]12C2 =>19/33.[/quote]

I think the answer to the first Q is not 4C2/2C12 as we already know one of the 2 cards in the king of spades. Thus it is 4C2 / 2 and final result is 1/22

For the 2nd question, if it is the prob to hold 2 kings answer is 1/11 as developed by "guest". If the question is at least 1 king, (4C2+4C1.8C1)/12C2 is correct

Great Anish, I see my mistake. I should have considered 1-8C2/12C2 as we are selecting two out of the card set. 1-8/12 would be the case if it was for selecting just one card.