And now, the answer to That Time Of Year Again!

[theweaselking]

Last time, you were asked a question:

Given a pair of randomly generated animals, each with a 50/50 chance of being male/female, you investigated and discovered that one of them was male. What are the odds that the other is male?

If you said "Dice don't have a memory, babies aren't entangled, any random baby is male so the answer is 50%", you are wrong. You win nothing!
If you said "1/3", you are correct. You also win nothing!


The trick here is that, had the babies been born separately and considered separately, people who thought the probabilities weren't related would be correct. However, we're not serially generating random Velocibabies. We've generated A PAIR of random babies, and then filtered the possible results of random pairs of babies, and THEN looked at possibilities.

When you generate two random babies, the possibilities are:
1. Female/Female
2. Female/Male
3. Male/Female
4. Male/Male

Each of those possibilities is equally likely. With me so far?

By examining one baby (you don't know which baby), and determining that the baby is male, you *eliminate* some of your sample set. You KNOW you didn't get Female/Female. However, you still don't know which of F/M, M/F, or M/M you're in.

And, at the same time, those three results are equally likely. And in two of the three results, the other baby is Female. In only one of the possible sets of results is the other baby Male.

As such, the real question being asked is "given what we know, what are the odds that we're in the sample set with both babies being Male". And that is 1/3.