Suppose I have a deck of 26 black and 26 red cards. I randomly choose 26 cards from this deck and I look at the first two cards. What is the probability that both cards are black?
I think the probability is $$ \frac{1}{2}\frac{25}{51} = \frac{25}{102}$$ since we are choosing 26 cards randomly and this is equivalent to having a total deck. Is my reasoning correct?
On
YES!
The experiment is like picking one card at random from the deck, and then another.
How likely are both black? Use the rule that says P(A and B) = P(A)P(B|A) where A and B are the probabilities that the first is black, and that the second is black.
How likely is it that the first is black? 1/2
Given that the first is black, how likely is it that the second draw is too? only 51 cards left, of which 25 are black... 25/51.
wrong there are two cases
first, withdrawing with replacement will be 26/52*26/52=0.25
Secondly, withdrawing without replacement will be 26/52*25/51=0.245