In a group of 20 people, 12 have brown eyes and 8 have blue eyes. If we randomly select two people from the group, what is the probability that both have blue eyes?
Let's reason through this problem step-by-step:

1. We know there are 20 people in total, with 12 having brown eyes and 8 having blue eyes.
2. The probability of selecting one person with blue eyes would be the number of blue-eyed people divided by the total number of people, which is 8/20 or 4/10 (simplified).
3. After selecting one blue-eyed person, there will now be 19 people left in the group, with 7 of them having blue eyes.
4. The probability of selecting another person with blue eyes after the first selection would then be 7/19.
5. To find the probability of both events happening together (i.e., selecting two blue-eyed people), we multiply their individual probabilities: (4/10) * (7/19).

The final answer is (4/10) * (7/19), which simplifies to 14/95.