Probability Problem, possibly bayes...

[bumblingchronic]

I am stuck on a question that I really believe should be quite simple.

Consider a coin with an unknown probability p of landing heads. Suppose that it istossed 10 times and lands heads on 4 occasions.


(i) [5 marks] What is the maximum likelihood estimate for p?


(ii) [5 marks] If we used a uniform prior for p, what would the mean of the posterior be
after observing the data?

Obviously the answer to part i is 4/10, but I don't know how to get the answer to part ii. I do know the answer is 5/12 however.

Any help would be greatly appreciated.