Chapter 10.4, Problem 15E

To determine

Tocalculate:

The probability of randomly selected tree has both a disease and damaged by insects.

Answer to Problem 15E

The probability of randomly selected tree has both a disease and damaged by insects is $0.1$ .

Explanation of Solution

Given information:

Total group of trees $=40$

Trees having disease or being damaged $=34$

Trees having disease $=18$

Trees being damaged by insects $=20$

Formula used:

  $P\left(AorB\right)=P\left(A\right)+P\left(B\right)-P\left(AandB\right)$

Calculation:

There are $40$ trees in a forest. Assume that event $A$ denote trees having a diseaseand event $B$ denote trees damaged by insects.

It is further stated that $34$ trees have disease or being damaged by insects. Then, with the help of given information given probability as follows:

  $P\left(A\right)=\frac{18}{40},P\left(B\right)=\frac{20}{40},P\left(AorB\right)=\frac{34}{40}$

Then, the required probability of $A$ or $B$ is as given follows:

  $\begin{array}{l}P\left(AorB\right)=P\left(A\right)+P\left(B\right)-P\left(AandB\right)\\ \frac{34}{40}=\frac{18}{40}+\frac{20}{40}-P\left(AandB\right)\\ =0.1\end{array}$

Hence, the answer is $0.1$ .

So, the probability of randomly selected tree has both a disease and damaged by insects is $0.1$ .