maybe you can help me out. The following holds: There is a deck of 52 cards. 13 clubs, 13 spades, 13 hearts, 13 diamonds). Normal deck of cards. Nothing special.
And now the following happens. I draw a card, and put it away, without looking at it. I then draw 2 more cards and look at them. Each of those 2 cards were spades. And now I want to know, given this information, what the probability is, that the first card I didn't look at, was spades as well.
I don't even know, how to start, notation wise. Like P(first drawn card = spades| 2nd and 3rd drawn card = spades)? And normally, should it not just be P(first card = spades) =13/52? But I feel, that would be wrong here.
I would try to calc 13/52 x 12/51 x 11/50 = 0.0129. So that would be 1.3% But that doesn't consider the information properly, I think.