SOLUTION: 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 a

Question 135683: 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.
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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.
----------------------------------------------------------------------------
There are 12 cards in the jack/queen/king pool and 40 cards not in the pool.
-----------------
P(pick a jack or queen or king) = 1 - prob(no jack/queen/king) in three draws)
1 - (40C3/52C3) = 1-0.4470588... = 0.5529411...
====================================================
Cheers,
StanH.
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

Give me the name of this guy who told you it was 70%. I want to play poker with him.
RELATED QUESTIONS
I would like to know what the probability of taking three cards from a full deck of cards (answered by solver91311)
I am solving this problem: Suppose that you take all of the black cards out of a... (answered by stanbon)
I am solving this problem: Suppose that you take all of the black cards out of a... (answered by stanbon)
1. Two cards are selected without replacement from a usual deck of 52 cards. [A deck of... (answered by stanbon)
My Question: If THREE cards are dealt from a 52 card deck, what is the probability that... (answered by natolino_2017,math_helper)
what is the probability of drawing 5 black cards from a deck if you know there are at... (answered by ikleyn)
WHAT IS THE PROBABILITY OF DRAWING EITHER A JACK OR A HEART FROM A FULL DECK OF 52 CARDS? (answered by josmiceli)
hi i need help with this problem. i need help on this question: five cards are drawn... (answered by stanbon)
If four cards are chosen at random from a standard deck of playing cards, how many... (answered by stanbon)