You observe a $50$ price for a non$-$dividend$-$paying stock. The call option has two years to mature, the periodically compounded risk$-$free interest rate is $5\%,$ the exercise price is $50.$ The stock is expected to increase by $35\mathrm{.}6\%$ or decrease by $26\%.$

a$.$ Calculate the probability of an up move based on the risk$-$neutral probability.

b$.$ Using a $2-$year binomial model, calculate the current European call option value. Show all your work!