Question 7 Winston 176 Problem 3 Modified A forest consists

Question 7. [Winston 17.6 Problem 3 Modified] A forest consists of two types of trees: those that are 0-5 ft and those that are taller than 5 ft. Each year, 40% of all 0-5 ft tall trees die, 10% are sold for $20 each, 30% stay between 0 and 5 ft, and 20% grow to be more than 5 ft. Each year, 50% of all trees taller than 5 ft are sold for $50, 20% are sold for $30, and 30% remain in the forest.

(a) What is the probability that a 0-5 ft tall tree will die before being sold?

(b) If a tree (less than 5 ft) is planted, what is the expected revenue earned from that tree?

Solution

(a) What is the probability that a 0-5 ft tall tree will die before being sold?

0.40

(b) If a tree (less than 5 ft) is planted, what is the expected revenue earned from that tree?

0.10 * 20 + 0.20 [0.50 * 50 + 0.20 * 0.30]

2+(25+6)*0.20

2+6.2

8.2

expected revenue earned from that tree = 8.2