Suppose a box contains 5 white balls and 5 black balls.
If you want to extract a ball and then another:
What is the probability of getting a black ball and then a black one?
I think that this is the answer:
Let $A:$ get a black ball in the first extraction, $B:$ get a black ball in the second extraction. Then: $P(A)=\frac{5}{10}$ and $P(B|A)=\frac{P(A\cap B)}{P(A)}=\frac{\frac{4}{9}}{\frac{1}{2}}=\frac{8}{9}$
Is this correct?
Now, If you want to extract two balls at the same time: what is the probability that both are black? Is exactly the same probability of the first question? Why?
Thanks for your help.