At time 0.5, the price of $1 par of a zero maturing at time 1 will be either $0.97 or $0.99. Consider two other assets. Asset A pays off $1 at time 0.5 if the price of the zero maturing at time 1 is $0.97 and pays off 0, otherwise. Asset B pays off $1 at time 0.5 if the price of the zero maturing at time 1 is $0.99 and pays off 0, otherwise. The price today of Asset A is $0.48 and the price of Asset B is $0.49. This information is summarized above.

a) What is the price today of the zero maturing at time 1 in the absence of arbitrage? b) What is the price today of the zero maturing at time 0.5 in the absence of arbitrage? c) What are the risk-neutral probabilities of the two possible time 0.5 values of the zero maturing at time 1?

Please explain in detail