SOLUTION: Two cards individually are drawn from a deck of 52 cards. Calculate the probability that the draw will include an ace and a nine.

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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