Before the Exxon Valdez accident, the risk of oil tanker leakage was thought to be minimal. At the time, the savings of using single hull tankers to Exxon was $$45$ million with few accidents in $6$ years and $$110$ million with no accidents resulting in a present value of expected savings of $$50$ million.

a$)$ What was the probability of no accidents prior to the Valdez accident? Assume a discount rate of $10\%.$

$E(V_0)=\frac{p{r}_u(V_u)+(1-p{r}_u)(V_d)}{(1+r_t{)}^T},p{r}_u=\frac{E(V_0)(1+r_t{)}^T-V_d}{(V_u-V_d)}$