1. Dutch Elm disease is caused by a harmful fungus that is spread by bark beetles. Roughly 50% of elms in the US have been affected by the disease. The most common symptom is early autumnal yellowing of the leaves. But sometimes this yellowing is a perfectly healthy response to the amount of water available to the root systems. 80% of trees with Dutch Elm disease have early yellowing, and 20% of trees without it have early yellowing. You come upon an elm with early yellowing leaves.

(a) What's the probability that it has Dutch Elm disease?

On average, elms with Dutch Elm disease die about 40 years earlier than trees without the disease. A fungus herbicide can cure the tree from the disease. But if it's applied to trees that don't have the disease, it's quite bad - on average it takes about 60 years off the tree's lifespan.

(b) Assume your only goal is for the tree to live as long as possible. Say (i) whether you should you apply the herbicide or not, and (ii) the difference in expected lifespan between the two options.