Two cards are drawn without replacement from a standard deck of 52 cards. What is the probability that both cards are spades?

1/17; no, they are dependent events
3/52; no, they are dependent events

Question

Two cards are drawn without replacement from a standard deck of 52 cards. What is the probability that both cards are spades? 

1/17; no, they are dependent events
3/52; no, they are dependent events

marihelenh · Answer

Question first, are those answer choices?

anonymous · Answer

Yes. There are four choices, but I already ruled the other ones out

marihelenh · Answer

what were the other two if i may ask. I'm getting a different answer.

anonymous · Answer

1/16; yes, they are independent events
25/52; yes, they are independent events

marihelenh · Answer

You can just give me the first part

marihelenh · Answer

Ok, I see what you mean

anonymous · Answer

OK :) do you think you can explain how you got your answer, as well?

misty1212 · Answer

hmm

misty1212 · Answer

HI!

misty1212 · Answer

it is "without replacement" right?

marihelenh · Answer

Ok, so the card isn't replaced. To draw a spade the first time, you have a 13/52 chance. And then to draw a spade the second time, you have a 12/52 chance.

anonymous · Answer

Hi and yes!

marihelenh · Answer

So, what you want to do first, is multiply 12 and 13.

misty1212 · Answer

no, actually the second time, given that the first one is a spade, it is $\frac{12}{51}$

marihelenh · Answer

However, we also need to know the sample space, so you would multiply 52 and 51 (when one card is removed).

anonymous · Answer

OK and the fact that it says, "without replacement" that means that it is dependent right?

marihelenh · Answer

So, you would put the spades over the sample space:

$$\frac{ 12*13 }{ 52*51 }$$

marihelenh · Answer

Yes, @misty1212, was right, it should have been 12/51

anonymous · Answer

She said 11/51 though

marihelenh · Answer

But otherwise, there is your setup. It will give you your final answer

marihelenh · Answer

She said 12/51. I don't see an 11/51 in here. Trust me, this is correct. If you still don't get it, look here for more info and detail http://math.stackexchange.com/questions/1469636/two-cards-are-drawn-without-replacement-from-an-ordinary-deck-of-52-cards-what

anonymous · Answer

So which numbers, do I use?

marihelenh · Answer

The equation I gave you

anonymous · Answer

Oh sorry I see :)

anonymous · Answer

Is 1/17 right? @marihelenh

marihelenh · Answer

Yep!

anonymous · Answer

OK thanks!