2 cards drawn from a standard 52 deck, what is probability both are the same suit?

Question

i dont really want the answer, i want to know how to do it. I think it has to do with combination because order doesn't matter, but i'm not sure how to make the formula

Answer 1

12 in 51

Draw one card any card.
Now what is the chance that the second card is of the same suit.
Say the first card is a heart. There are 12 hearts left in a deck that now have 51 cards so 12/51.

Answer 2

When you pick the first card, does it matter what card it is? Anything you choose as a first card will still allow you to have the second card match it.

Once you have the first card chosen, what is the probability that the second card will be the same suit as the first? Isn't this the same problem just worded differently?

To find the probability, take the number of possibilities for meeting the condition and divide it by the total number of possibilities. In this case, there are 12 cards in the deck that match the suit of the first card chosen. There are 51 cards left in the deck. So, the probability is 12/51.

Combinations are typically used in probability, and if you were picking 3 cards and you wanted 2 of the same suit then you would use combinations. Technically we used them too, but it was easy enough to calculate the combinations because we were only choosing one :)

Answer 3

Well, the first card can be any suit, so the probability of drawing a card that has a suit is 52/52, or 1. The second card has to be the same suit as the first card, so the chances that this will happen are 12(cards remaining of that suit)/51(total cards remaining). To find the probability of both happening, you multiply them together. 1 * 12/51= 12/51.

Answer 4

It doesn't matter what the 1st card is. When you are drawing the 2nd, there are 51 cards, 12 of which are the same suit as the 1st 1, so the probability is 12/51=4/17=.235

Answer 5

Take out the first card which is the one you need to match. You don't care which suit it is since you want to match it regardless.

Now you are ready to take out one more card. There are now 12 more cards of that same suit left in the deck and 51 cards left in the deck. That makes it 12 chances out of 51 for a match. If you take out one of those 12 you have the match.

Answer 6

Lets do it simply:
The first card can be anything.

The second you draw (From 51!) must be the same
Suit as the first (12 remaining)

So the probability is simply (12/51)