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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

Expert verified

Part (a) The probability is 0.24

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

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

Step by step solution

01

Part (a) Step 1. Concept

Theprobabilityofanevent=numberoffavorableoutcomestotalnumberofoutcomes

02

Part (a) Step 2. Calculation

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

P(DamagedbyDeer)=60+76+44+29/60+76+44+29+151+158+177+176.=209/871=0.24

0.24 is the required probability.

03

Part (b) Step 1. Calculation

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

P(Damage|None)=60211=0.28

P(Damage|<1/3)=76234=0.32

P(Damage|1/3or2/3)=44221=0.20

P(Damage|>2/3)=29205=0.14

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

04

Part (c) Step 1. Calculation

It is clear from parts (a) and (b) that P(Damage)=0.24P(Damage|None)=0.28

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.

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