So, I am having a problem with this in that the method I use gives two completely separate answers.
Two cards are selected from a deck of $52$ playing cards. What is the probability they constitute a pair (that is, that they are of the same denomination)?
So, for the first method I reason this.
The first card picked has a $13/52$ chance of being in some suit. The second card picked has probability $12/51$ of being in the same suit.
So... The probability should be $(13/52)(12/52) = 3/52$.
The other method is by combinatorics.
I have $52 \cdot 51$ one ways of creating a pair of cards. But I have $13 \cdot 12$ different ways of creating a pair of the same suit. Now to me, the logical thing to do is to multiply this number by $4$, because I would have to count each valid pair from each suit.
This would give me
$$\frac{4 \cdot 12 \cdot 13}{52 \cdot 51}$$
What's wrong with the reasoning on the second one?
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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) (Show Source): You can put this solution on YOUR website! Answer by Fombitz(32382) You can put this solution on YOUR
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Two cards are draw at random from a well shuffled pack of 52cards. Find the probability that:
• Both are the same color
• Both are the different color
The deck has cards of two colors: red and black. The probability to draw a black color is "\\frac{26}{52}=0.5" and the same is the probability to draw a red color. The probability that two cards have a red color is: "\\frac{26}{52}\\cdot\\frac{25}{51}\\approx0.2451". The same is the probability that two cards have a black color. We used the multiplication rule (//www.statisticshowto.com/multiplication-rule-probability/) The probability cards have the same color is: "0.2451\\cdot2=0.4902". The probability that both cards have the different color is: "1-0.4902=0.5098"
Answer: the probability that two cards have the same color is: 0.4902; the probability that both cards have the different color is: 0.5098.