To find the ratio of true positives to false positives, let's break down the problem step by step:
1. Understand the Given Data:
- True Positive Rate: 88% (When there is lightning, the detector activates 88% of the time).
- False Positive Rate: 7% (When there is no lightning, the detector activates 7% of the time).
2. Calculate the Ratio:
We need to determine the ratio of true positives to false positives. This can be calculated using the formula:
[tex]\[
\text{Ratio of True Positives to False Positives} = \frac{\text{True Positive Rate}}{\text{False Positive Rate}}
\][/tex]
Substituting the given values:
[tex]\[
\text{Ratio of True Positives to False Positives} = \frac{88\%}{7\%}
\][/tex]
3. Perform the Division:
[tex]\[
\frac{88}{7} \approx 12.571428571428571
\][/tex]
4. Round the Ratio to One Decimal Place:
When we round 12.571428571428571 to one decimal place, we get 12.6.
Therefore, the ratio of true positives to false positives in this scenario, rounded to one decimal place, is [tex]\( \boxed{12.6} \)[/tex].
