A teacher has a box containing 20 red pens, 30 blue pens, and 40 black pens. If she randomly picks one pen from the box without looking, what is the probability that the pen is not black?
Let's analyze this problem step-by-step:

1. There are a total of 20 red pens + 30 blue pens + 40 black pens = 90 pens in the box.
2. We want to find the probability that the pen picked is not black, which means it could be either red or blue.
3. There are 20 red pens and 30 blue pens, so there are 20 + 30 = 50 non-black pens in the box.
4. The probability of picking a non-black pen is the ratio of non-black pens to the total number of pens: 50/90.

Hence, the probability of picking a pen that is not black is 50/90, which simplifies to 5/9.