A box contains 10 black balls, 15 white balls, and 5 yellow balls. If you randomly pick two balls without replacement, what is the probability that at least one ball is black?
The probability that at least one ball is black is 19/29 or approximately 65.52%.

Here's the reasoning:

1. Instead of calculating the probability that at least one ball is black, it's easier to calculate the probability that neither ball is black and then subtract this from 1.
2. The probability that the first ball picked is not black is 20/30 (since there are 15 white balls and 5 yellow balls).
3. If the first ball picked is not black, there will be 19 non-black balls left in the box and a total of 29 balls remaining. So, the probability that the second ball picked is also not black is 19/29.
4. Therefore, the probability that both balls picked are not black is (20/30) * (19/29), which simplifies to 10/29 or approximately 34.48%.
5. To find the probability that at least one ball is black, we subtract the probability that neither ball is black from 1: 1 - 10/29 = 19/29 or approximately 65.52%.