You have traveled to london (a "rainy city") and forgotten your umbrella. you have an important interview the next day, for which the probability that it will rain is 40%. if you get caught in the rain you will do $75 of damage to your expensive suit. the cost of an umbrella is $25. draw the decision tree for this problem. what should you do? how sensitive is your decision to (a) a 10% change in probability of rain; (b) a 20% change in probability of rain.