Final answer:
Calculate the probability of a driver using a cell phone while driving or having no violations in the past year using the union probability formula, incorporating probabilities for each individual event and their intersection.
Step-by-step explanation:
To calculate the probability in question, we must analyze the fictional data provided in the study of speeding violations and cell phone usage while driving. Specifically, the probability of interest is the chance that a driver either uses their cell phone while driving, has no driving violations in the past year, or both. This requires the use of set theory and specifically the calculation of a union probability. The formula for the union of two events A (cell phone use while driving) and B (no violation in the past year) is P(A ∪ B) = P(A) + P(B) - P(A ∩ B).
Assuming we have the probabilities for P(A), P(B), and P(A ∩ B) from the study data, we can plug these values into the formula to find our answer. It's essential to remember that P(A ∩ B) represents the participants who fall into both categories. After computing the formula, we will obtain the probability that describes the behavior of the studied drivers with respect to these two variables.