Is the Strategy Real or Lucky

A researcher shows you a strategy with $60$ winning trades out of $100$. Take the world to contain only two kinds of strategy: real ones, which win each independent trade with probability $0.55$, and worthless ones, which win with probability $0.50$. From experience you believe only $1$ submitted strategy in $5$ is real.

(a) After seeing $60$ wins in $100$ trades, what is the probability this strategy is real? (b) The researcher points out the result is "statistically significant at two sigma." Reconcile that with your answer. (c) Roughly how many trades would a genuinely real strategy need before you were $95\%$ convinced?