[mattstat]

In my case, it is.

But how about Mr B? Here’s a twist: Mr B has two children, one of whom is a son born on 29 June. What is the probability that Mr B has two boys?

[mattstat]

I forgot to say about the twist: ignore leap years.

[dangus]

Still exactly 1/3.

[KarlInOhio]

But how about Mr B? Here’s a twist: Mr B has two children, one of whom is a son born on 29 June. What is the probability that Mr B has two boys?

If you ignore twins it will be 729/1459 or 49.9657%. Very close to 50% because the odds of having both born on 29 June is very low.

I don't think ignoring twins is valid in this case because you are far more likely to have twins (I saw about 3%, but I don't know if that is 3% of births or pregnancies) than just randomly sharing birthdays (0.28% chance).