Chapter 5, Problem 9CRE

a.

To determine

To find: The probability that randomly chosen seedling has been damaged by deer.

Answer to Problem 9CRE

The probability is 0.24

Explanation of Solution

Given:

Table is:

Cover	Yes	No
None	60	151
<1/3	76	158
1/3 to 2/3	44	177
>2/3	29	176

Calculation:

The probability that randomly chosen seedling has been damaged by deer is calculated as:

  $\begin{array}{c}P\left(\text{Damaged by Deer}\right)=\frac{60+76+44+29}{60+76+44+29+151+158+177+176}\\ =\frac{209}{871}\\ =0.24\end{array}$

The required probability is 0.24.

b.

To determine

To find: The probability that randomly chosen seedling has been damaged given each cover.

Answer to Problem 9CRE

The probabilities are 0.28, 0.32, 0.20, 0.14 respectively.

Explanation of Solution

Calculation:

The probability that randomly chosen seedling has been damaged given each cover can be calculated as:

  $\begin{array}{l}P\left(\text{Damage| None}\right)=\frac{60}{211}=0.28\\ P\left(\text{Damage| <1/3}\right)=\frac{76}{234}=0.32\\ P\left(\text{Damage| 1/3 or 2/3}\right)=\frac{44}{221}=0.20\\ P\left(\text{Damage| > 2/3}\right)=\frac{29}{205}=0.14\end{array}$

The required probabilities are 0.28, 0.32, 0.20, 0.14 respectively.

c.

To determine

To find: Whether the known amount of cover is changing the probability of deer damage

Answer to Problem 9CRE

Yes, it is changing the probabilities.

Explanation of Solution

From part (a) and (b), it is known that

  $\begin{array}{l}P\left(\text{Damage}\right)=0.24\\ P\left(\text{Damage|None}\right)=0.28\end{array}$

The probabilities are not same. Thus, the events cannot be said independent which implies that the known amount of cover is changing the probability of deer damage.