Question: In a particular forest, a total of 292 trees were examined to determine if they were diseased, and…

In a particular forest, a total of 292 trees were examined to determine if they were diseased, and 42 of them showed signs of disease. What is an appropriate estimation for the probability a tree in this forest is diseased?

• 0.14
• 0.42
• 0.69
• 6.95

Solution

To estimate the probability that a tree in this forest is diseased, we calculate the ratio of the number of diseased trees to the total number of trees examined. Number of diseased trees = 42 Total number of trees examined = 292 The probability \( P \) is given by the formula: \[ P = \frac{\text{Number of diseased trees}}{\text{Total number of trees examined}} \] \[ P = \frac{42}{292} \] Now, calculate the fraction: \[ P = \frac{42}{292} \approx 0.144 \] Therefore, the estimated probability that a tree in this forest is diseased is approximately 0.14.