Creating Semi-Randomized Characters

To demonstrate how this works, let's create a third child of Hermione and Ron Weasley, a daughter named Margaret. We'll take our coin, and in the classic Roman tradition, designate heads as "yes" and tails as "no." And we shall begin:

"Does Margaret share any of her mother's interests?" (Yes.)

"Does she share Hermione's love for studying?" (No.)

"Political activism?" (Yes.)

At this point, we get our die ready and ask the question: "How good is Margaret at being a political activist?" (6 - extremely good.)

Now, back to the coin: "Does she share any of her father's interests?" (No.)

"Does she excel in any of the Hogwarts core classes?" (No.)

"What about any electives?" (No.)

"Does she have any other skills of note?" (No.)

"Is there anything she's notably bad at? (No.)

(So Margaret is average when it comes with magic, but based on getting a 6 in being good at political activism, she's likely bursting with charisma and charm.)

"Is Margaret a Gryffindor?" (Yes.)

I deliberately asked whether she was in Gryffindor first because each toss has 50/50 odds, which means that you can't have a 1-in-4 chance for Gryffindor. Since it's canon that family members tend to end up in the same house, it's most reasonable to give Gryffindor the first go. Were I doing this for a child of Draco Malfoy, Slytherin would have been given the first shot.

Now we can tease out some of Margaret's tastes and preferences...

"Does Margaret like cats?" (No.)

"What about dogs?" (No.)

"Birds?" (Yes.)

"Any specific kind of bird?" (No.)

"How much does she like birds?" (3 - moderately interested. Perhaps she puts out a birdfeeder to attract birds to her home, or decorates her room/home in birds.)

This type of thing could go on as long as you want, but keep in mind that relying on random outcomes too much tends to create a nonsensical hodgepodge of a character, so it's advisable to fill in certain gaps and blanks as common sense dictates. For example, in the Harry Potter universe, wand woods and wand cores tend to align with specific character traits, so it wouldn't make a lot of sense to randomize a wand for a character you've built up already. (On the other hand, feel free to build up a character around a randomized wand.)

For a second example, let's make a random guy named Jim Whiffits.

"Is Jim an adult?" (No.)

"Is he a teenager?" (Yes.)

"Does Jim have siblings?" (No.)

"Is Jim academically inclined?" (Yes.)

"Does he have any specific interests?" (No.)

...So in other words, Jim Whiffits likes to read about anything and everything!

Does he have any outstanding skills? (No.)

Is there anything he's really bad at? (No.)

So Jimmy's a classic jack-of-all-trades-but-master-of-none. Now, die time!

"What's Jim's economic level?" (4 - upper end of the middle class.)

"How strong is Jim, physically?" (4 - slightly stronger than average.)

And back to the coin...

"Does Jim conceal any secret he doesn't want anyone to know about?" (Yes.)

"Is it about Jim personally?" (No.)

"Is it about someone he knows?" (No.)

"Is it something Jim is doing?" (No.)

"Is it paranormal in nature?" (Yes.)

"Is it in or around Jim's home?" (No.)

"Is it in or around Jim's school?" (Yes.)

By now you should have a pretty good idea of how this works. Also, you can use this method for worldbuilding, coming up with plot scenarios, artistic designs, etc.