Question 1150347: Two cards individually are drawn from a deck of 52 cards. Calculate the probability that the draw will include an ace and a nine.
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
First solution method: using the probabilities that each card, drawn one at a time, can produce the desired result.
The first card can be either an ace or a nine -- probability 8/52 = 2/13.
The second card can only be a nine if the first card was an ace, or vice versa -- probability 4/51.
P(an ace and a nine) = (2/13)*(4/51) = 8/663.
That first solution method is easily used to find the answer for this particular problem.
For more complicated probability problems, you might need a more sophisticated method. For this problem, it could look something like this:
You are choosing 2 of the 52 cards; the desired outcome is you get 1 of the 4 aces, 1 of the 4 nines, and 0 of the other 44 cards. The probability is
C(4,1)*C(4,1)*C(44,0) (4*4*1) 16 8 8
--------------------- = --------- = ------- = ----- = -----
C(52,2) (52*51) 26*51 13*51 663
-------
(2*1)
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