Question

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 0–5ft 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?

Answer 1

a. 40%

b. $3.2

Explanation:

a. As each year 40% of all 0-5ft trees die and other 10% are sold. That means the probability of a 0-5ft tall tree will die before being sold is 40%.

b. The probability of a tree that grows from 0-5ft to more than 5 ft AND get sold is

20% * 20% = 0.2 * 0.2 = 0.04

The probability that a tree stays the same and gets sold in the following year is small and can be neglected.

The expected value to earn from a planted tree is the combination of the expected value of its being sold at between 0-5ft and when it's more than 5 ft

`E = E_1 + E_2 = 20*0.1 + 0.04*30 = 2 + 1.2 = \$3.2`