Touch probability for a stock

A stock trades at $100 with 20% annual volatility. Model its log price as driftless Brownian motion, $\ln(S_t/100) = 0.2\,W_t$. (a) What is the probability that it trades at or above $120 at some point in the next year? (b) Compare this with the probability that it ends the year above $120. (c) With zero interest rates, roughly how does a one-touch option that pays $1 if $120 is ever hit compare in price with a digital that pays $1 if the stock finishes above $120?