Question 611212: Problem: One card is drawn from a standard deck of cards and then a second card is drawn, find the probability of drawing a king and then another face card (King, Queen, or Jack)If:
A) The first card is replaced before the second is drawn
B) The first card is set aside and not replaced in the deck before the second card is drawn.
I know we are talking about permutation and commutation. I believe this is a commutation problem, but once they throw probability in their, I get confused on how to set up the problems. If you could walk me through the problem so I can show my work and get a better understanding that would be great.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Problem: One card is drawn from a standard deck of cards and then a second card is drawn, find the probability of drawing a king and then another face card (King, Queen, or Jack)
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Keep in mind the basic idea of probability:
P(success) = # of ways to succeed/(# of possible outcomes)
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Note: Combinations and Permutations are simple 2 ways to
help you count the # of successes and the # of possible
outcomes.
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If:
A) The first card is replaced before the second is drawn
# of ways to draw a King: 4
# of possible outcomes: 52
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P(draw a King) = 4/52 = 1/13
P(draw a King twice with replacement) = (1/13)^2 = 1/169
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B) The first card is set aside and not replaced in the deck before the second card is drawn.
P(draw 2 Kings without replacement) = (4/52)(3/51) = 12/2652 = 1/221
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You could also get the B answer as follows:
# of ways to draw 2 Kings: 4C2 = 6
# of ways to draw 2 cards randomly: 52C2 = 1326
P(draw 2 Kings without replacement) = 6/1326 = 1/221
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Cheers,
Stan H.
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