Question 198807: two cards are drawn from a standard deck of cards. find the probability that a king or red card is drawn.
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
There are actually two different answers to this question depending on whether or not you put the first drawn card back in the deck before you draw the second one.
The easiest way to calculate this probability is to calculate the probability of NOT drawing either a King or a red card in two draws and then subtracting that probability from 1.
Without Replacement.
There are 26 red cards in a deck of 52, two of which are Kings, and then there are 2 black Kings, for a total of 28 possible. That means that there are 24 cards remaining that are NOT either a King or a red card. So the probability that you do NOT draw a King or a red card on the first draw is 
Now, given that you were 'successful' -- that is you did not draw a King or a red card on the first draw, then there would remain 51 cards to choose from of which 23 would be not a King or red. So the probability, given non-replacement, is 
And the overall probability is the product of the probabilities of these two events:
\left(\frac{23}{51}\right))
But since we actually want the probability of the opposite case, we have to subtract from 1:
\left(\frac{23}{51}\right))
With replacement.
If we put the first drawn card back into the deck before selecting the second one, then the probability of not getting a King or red card is identical for each of the draws, so our probability, for getting either a King or a red suit is:
^2)
You get to do your own arithmetic.
John
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