Question

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? Justify your answer.

• When appropriate, use the multiplication rule for independent events to compute probabilities.

Short answer

Part (a) The probability is $0.24$

Part (b) The probabilities are $0.28,0.32,0.20,0.14$respectively.

Part (c) Yes, it is changing the probabilities.

Step-by-step solution

Part (a) Step 1. Concept

$Theprobabilityofanevent=\frac{numberoffavorableoutcomes}{totalnumberofoutcomes}$

Part (a) Step 2. Calculation

The probability that a deer has harmed a randomly chosen seedling is computed as follows:

$$\begin{gathered} P(DamagedbyDeer)=60+76+44+29/60+76+44+29+151+158+177+176. \\ =209/871 \\ =0.24 \end{gathered}$$

$0.24$ is the required probability.

Part (b) Step 1. Calculation

Given each cover, the likelihood that a randomly picked seedling has been harmed can be computed as follows:

$P\left(Damage\right|None)=\frac{60}{211}=0.28$

$P\left(Damage\right|<1/3)=\frac{76}{234}=0.32$

$P\left(Damage\right|1/3or2/3)=\frac{44}{221}=0.20$

$P\left(Damage\right|>2/3)=\frac{29}{205}=0.14$

$0.28,0.32,0.20$ and $0.14$ are the needed probability, respectively.

Part (c) Step 1. Calculation

It is clear from parts (a) and (b) that $$\begin{gathered} P\left(Damage\right)=0.24 \\ P\left(Damage\right|None)=0.28 \end{gathered}$$

The chances aren't the same for everyone. As a result, the events cannot be stated to be independent, implying that the known amount of cover affects the likelihood of deer damage.