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Expert: - 10/6/2009


Question
Hi i am studying probability at the moment and i got stuck on this question. I just can't work out the theory to get the right answer. The question is "Two cards are chosen at random from a deck. What is the probability of getting a diamond and a 5 without replacement?"  The answer is meant to be 1/68 or 0.014705882.
Thanks for your help especially if you can work out how to do it.

Answer

Chance of a diamond an
The chance has to be viewed as three possibilities.
One: The five of diamonds is not drawn.
Two: The five of diamonds is drawn 1st.
Three: The five of diamonds is drawn 2nd.

One: (12/52)(3/52), since the 5 of diamonds is not drawn,
so that's the count without the 5 as a diamond and the 5 drawn as another suit.

Two: (1/52)(3/52), since the 1st card is the 5 of diamonds and the second is not.

Three: (12/52)(1/52), since the 1st is not the 5, but the second card is.

Let me fiddle in Excell for a minute...
... I believe it is 51/(52*52). Here, I will import the file to show you.
Open up the file I'm giving to you.

Actually, I believe that should be *2, since I only looked at one way of it happening.
    Questioner's Rating
    Rating(1-10)Knowledgeability = 6Clarity of Response = 7Politeness = 10
    CommentThank you for looking but i still don't understand the answer you gave me. The probability changes for the second draw from the deck as you will be picking from 51 cards rather than 52 cards the second time, however it makes sense that you only have a 3/52 or 12/52 of getting a 5 or a diamond. It has given me another way to try and work it out but i do not believe you have given me the right answer. If you prove me wrong though then i am more than happy, honestly this question is driving me insane.


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Scott A Wilson

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