SOLUTION: How do you solve: Two cards are drawn, without replacement, from a standard 52-card deck. Find the probability that both cards are the same color. Thank you!

Algebra ->  Probability-and-statistics -> SOLUTION: How do you solve: Two cards are drawn, without replacement, from a standard 52-card deck. Find the probability that both cards are the same color. Thank you!       Log On


   



Question 371923: How do you solve:
Two cards are drawn, without replacement, from a standard 52-card deck. Find the probability that both cards are the same color.
Thank you!

Found 2 solutions by stanbon, Fombitz:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
How do you solve:
Two cards are drawn, without replacement, from a standard 52-card deck. Find the probability that both cards are the same color.
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Pick a color: 2 ways
Pick two cards without replacement: 26C2 = (26*25)/(1*2) = 325
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Pick two cards randomly: 52C2
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P(2 cards same color) = [2*325]/[52C2] = 0.4902
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Cheers,
Stan H.

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1st Red:P%28R%29=26%2F52=1%2F2
2nd Red:P%28R%29=25%2F51
P%28R%2CR%29=%281%2F2%29%2825%2F51%29
P%28R%2CR%29=25%2F102
Since there are the same number of reds and blacks.
P%28B%2CB%29=25%2F102
So the probability that the cards are the same color is,
P=P%28R%2CR%29%2BP%28B%2CB%29
P=25%2F102%2B25%2F102
highlight%28P=25%2F51%29