How long a record proves skill?

Use a prior probability of skill of 1% (Barber et al.). A skilled trader has true net per-trade Sharpe 0.1; an unskilled one 0. (a) Show that if you only learn whether the $t$-statistic exceeded 2, the posterior probability of skill can never exceed about 31%, however many trades are observed. (b) If instead you observe the $t$-statistic itself and it equals its expected value under skill, $t = 0.1\sqrt N$, how many trades are needed for a posterior of 50%?