コインを5回投げて5回表だったとき、表が出やすいコインと断定してよい確率を算出せよ。

More concretely, suppose we are interested in learning about the proba-
bility that a special coin lands heads when tossed. A priori we believe that
the coin is fair, so we assign θ an N (0, .25) prior. We toss the coin n = 5
times and obtain y = 5 heads.
Approximate the probability that the coin is biased toward heads.