More Biased?

Two coins are before you, say $1$ and $2$ , where coin $i$ has probability $p_i$ of heads. However, $p_1$ and $p_2$ are unknown to you, so you assign a Uniform prior to the values of $p_1$ and $p_2$ . You flip each coin $n$ times. For some $0 \leq k \leq n$ , coin $1$ shows heads $k$ times, while coin $2$ shows heads $n-k$ times. Find the probability that coin $2$ is more biased (i.e. has a probability that deviates from $1/2$ by a larger amount) than coin $1$ when $n = 30$ and $k = 10$ .

Answer format: round to 1 decimal place.