What is the probability of drawing two cards with the same color from a full deck of 52 cards?

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?

Click here to see ALL problems on Probability-and-statistics 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)     (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. ---- Pick a color: 2 ways Pick two cards without replacement: 26C2 = (26*25)/(1*2) = 325 ---- Pick two cards randomly: 52C2 ------------------------------------------------ P(2 cards same color) = [2*325]/[52C2] = 0.4902 ---- Cheers, Stan H. Answer by Fombitz(32382)     (Show Source): You can put this solution on YOUR website! 1st Red: 2nd Red: Since there are the same number of reds and blacks. So the probability that the cards are the same color is,

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 (https://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.

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