I would consider this as being a binomial distribution.
Let X be the event that a birthday matched.
X ~ B(10, 1/365)
Now you can find the probability that 3 out of 10 trials matched.
There are extensive resources on the internet and in this forum discussing the famous birthday paradox. It is clear to me how to calculate the probability of two people sharing a birthday i.e. P(s)=1-P(d). However i can't find any hints when it comes to estimating a probability without using formulae. Here goes:
I need to estimate a probability through trials. For each trial i generate two random birthdays. We know that, for each individual trial, the probability of a match is 1/365.
If i run this trial 10 times, and i observe that 3 times the birthdays matched, how do i relate that finding (a ratio 3/10) to 365?
note: this is homework