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.

#### Further Reading

- Statistics
- Descriptive Statistics
- Probability Theory
- Probability Distribution
- Hypothesis Testing
- Confidence interval
- Sample size determination
- Non-parametric Tests
- Correlation Regression
- Statistics Calculators