Question 114700
Two cards are drawn at random from a pack of 52 cards.The probability of getting at least a spade and an ace is?
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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<pre>