What is the probability of being born on:
a) the 10th of a month in a non-leap year
b) christmas day in a non-leap year
c) the 29th February

a) First, you need to be born on a non-leap year. What is this probability?
Then, you need to find the probability of being born on a 10th. How many 10th's are there in the number of non-leap years you chose in your probability?
Multiply those together to find the combined probability.

Can you try out the two others using the same principle?

I think (a) is a little simpler than what Unknown008 laid out. I believe what the OP means to ask is: if you are born in a non-leap year, what's the probability of being born on the 10th day of a month? To do this, first consider: how many 10th days of a month occur in a year? Second, how many days are in a non-leap year? Then divide the first by the second.

As for (c) - it could get a bit complicated, unless you make an assumption that leap years occur every 4th year. Feb 29 comes around once every 4 years, and the number of days in 4 years is 4 x 365 + 1 for the leap year. However, to truly get this right you should consider that in each span of 400 years there are three "missing" leap years - namely in those years that are divisible by 100 but not divisible by 400. Thus 1900 was not a leap year, but 2000 was. So over the course of 400 years there are 97 leap years, and the number of days in 400 years is 400 x 365 + 97.