Question 135687: I would like to know what the probability of taking three cards from a full deck of cards and having at least one jack,queen or king in the three cards. I have been told that the answer is 12/52 X 12/51 X 12/50 or about 70% and I feel that this is wrong. Please advise how to figure this out. Thank you.
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! Since the successful outcome is AT LEAST 1 face card in the 3 cards, you are faced with calculating the probability that there are exactly 3 face cards, then the probability that there are exactly 2, and then the probability that there is exactly 1, and then summing the result. This is a very convoluted and complex calculation.
Much easier is to realize that if you draw 3 cards the probability that at least one is a face card plus the probability that NONE of them are face cards is certainty -- there are no other possibilities. So, calculate the probability that NONE of them are face cards -- a fairly straightforward calculation -- and then subtract that value from 1.
In a standard deck of 52 cards, 3 times 4 = 12 of them are face cards and the other 40 are not face cards.
If I pick one card out of the deck, I have a 40/52 probability that it is not a face card. Presuming I am successful and draw a non-face on the first draw, I will now have a deck with 51 total cards and 39 non-face, so my probability of drawing a second card that is non-face given that the first card was non-face is 39/51. And the probability for the third card being non-face given that the first two were non-face is 38/50.
The total probability is then the product of these three probabilities:
 (rounded to the nearest 0.01)
So the probability that you will draw at least 1 face card in a three card draw is 
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