two cards are drawn without replacement from an ordinary deck, find the probability that the second is a spade, given that the first is a spade. What is the conditional probability?

Question

anonymous · Answer

I know I start with $$\frac{ 13 }{52 }$$

anonymous · Answer

then $$\frac{ 12 }{ 51 }$$

anonymous · Answer

That would be a good way to think about the probability of drawing a spade first, followed by a spade 2nd.

That's not exactly what they are asking you here though...

anonymous · Answer

You are given that the first is already a spade, so conditionally, since that is given, that probability is "1".  So all that is left is that you can view the rest of the deck as having 12 spades and there are 51 cards.

anonymous · Answer

So is my answer then,  $$\frac{ 12 }{ 51 }$$

anonymous · Answer

That's it!

anonymous · Answer

awesome thank you!

anonymous · Answer

Some questions, depending on how they are worded, are actually easier than they look at first.

anonymous · Answer

That is where I get in trouble!

anonymous · Answer

Does that make sense?  When they say "given that ...."  that means they are telling you that event can be assumed to have happened... you don't have to find it's probability since it is true (or as @tcarroll010 said, its probability is "1")

anonymous · Answer

Word problems can be tricky.  Patience and calmness will help a lot.