Posterior mean of a coin with a Beta(10,10) prior

The heads probability $P$ of a coin is unknown and is given the prior $P\sim\text{Beta}(10,10)$. The coin is then tossed $80$ times and lands heads $50$ times. What is the posterior mean of $P$ given these tosses?

$\tfrac35$. The Beta prior is conjugate to binomial data: the posterior is $\text{Beta}(10+50,\,10+30)=\text{Beta}(60,40)$, whose mean is $\tfrac{60}{100}=\tfrac35$.