Happy Birthday To Me!

Here's a simple, two-part puzzle suggested by the Minotaur's pal Arkamedes:

How many humans would you need to ask at random before there is a-better-than- average chance that at least two of them have the same birthday?

How many Martians would you need to ask at random before there is a-better-than-average chance that at least two of them have the same birthday?

For the purposes of this puzzle pretend that all birthdays are equally likely, and that Martians exist.