# Solved: Deer and pine seedlings. As suburban gardeners know, deer will eat almost anything green. In a study of pine seedlings a

#### ByDr. Raju Chaudhari

Oct 14, 2020

Deer and pine seedlings. As suburban gardeners know, deer will eat almost anything green. In a study of pine seedlings at an environmental center in Ohio, researchers noted how deer damage varied with how much of the seedling was covered by thorny undergrowth:

(a) What is the probability that a randomly selected seedling was damaged by deer?
(b) What are the conditional probabilities that a randomly selected seedling was damaged given each level of cover?
(c) Does knowing about the amount of thorny cover on a seedling change the probability of deer damage? If so, cover and damage are not independent.

### Solution

Thorny Cover Yes No Total
None 60 151 211
< 1/3 76 158 234
1/3 to 2/3 44 177 221
$>$ 2/3 29 176 205
Total 209 662 871

Let $A$ denote the event that the seedling was damaged by deer.

(a) The probability that a randomly selected seedling was damaged by deer is

$P(A)=\frac{209}{871} = 0.2399541$.

(b) The conditional probabilities that a randomly selected seedling was damaged given each level of cover is

$P(A|\text{ No cover})= \frac{60}{211} = 0.2843602$.

$P(A|\text{ < 1/3 cover})= \frac{76}{234} = 0.3247863$.

$P(A|\text{ 1/3 to 2/3 cover})= \frac{44}{221} = 0.199095$.

$P(A|\text{ > 2/3 cover})= \frac{29}{205} = 0.1414634$.

(c) The amount of thorny cover on a seedling change the probability of deer damage. The probability of getting damageed decreases with move covers. So cover and damage are not independent.