Aforest 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?

a. 40%

b. $3.2

Step-by-step 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

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.