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Risk-neutral probabilities

In the following interest rate tree, solve for the risk-neutral probabilities at time 0 and time 0.5, using the equation: p=(dt/d½ - dt+1d)/(dt+1u-dt+1d), where d½ is the discount rate (DR) at time=t. In addition, what is the value at time 0 of an option that pays $1.35 at t=1 in the down-down state.

t=0 t=0.5 t=1
d½,1 =0.972290 (DR) 1
d½,1½ =0.945094 d1,1½ =0.970403

d0,½ =0.973047 (DR)
d0,1 =0.947820 1
d0,1½ =0.922819 d1,1½ =0.974184

d½,1 =0.976086 (DR) 1
d½,1½ =0.952086 d1,1½ =0.97704


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