To be successful you must either:



1. Get one of the 12 non-ace spades and one of the 3 non-spade aces



There are 12×3 or 36 ways to do this.



2. Get the ace of spades and any of the other 51 cards.



There are 51 ways to do this.



So there are 36 + 51 or 87 ways to be successful.  That is the

numerator of the desired probability.



To calculate the denominator is just to find all the combinations

of 2 cards from the 52 card deck, which is C(52,2) or 1326.



So the desired probability is 87/1326 which reduces to 29/442.



Edwin







 

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