Final answer:
To calculate the probability of participants who use cell phones while driving or have no violation or both, you add the count from each category and subtract the overlap. It reflects the inclusion-exclusion principle in probability, ensuring accurate representation in the calculation.
Step-by-step explanation:
When calculating the probability of an event, one must consider all the possible outcomes that correspond to this event. In this scenario, to calculate the probability of participants who either use a cell phone while driving, have no violation in the past year, or both, you need to add the number of participants who fall into each category individually and then subtract those who are counted in both categories, to avoid double-counting.
For example, if you had a group of participants in your study where some used a cell phone while driving and some did not have any violations, you'd count each of these groups separately. Then you would subtract the number that overlaps, i.e., individuals who are both cell phone users while driving and have no violations, to find the total number of unique participants that fit the event criteria.
This type of problem represents a classic case of using the principle of inclusion and exclusion in probability, ensuring each participant is counted appropriately towards the total probability of the event in question.