Assume a two$-$period binomial tree model where each period the stock can either increase by $22\%,$ or fall by $16\%.$ Each step in the tree is $3$ months. The interest rate is $1\mathrm{.}8\%$ per year $($continuous compounding$).$ In this model, what is the risk$-$neutral probability that the stock price will go up once and drop once over the three periods?