Which of the following government services doesn't encourage community safety? Car seat installations, recycling, fire prevention programs,...

The answer may depend on if you expected to only "choose one" or if you are allowed to choose multiple answers to this question. 

At first glance, it is obvious that fire prevention programs and car seat installations have immediate effects on community safety. The first can prevent people from becoming trapped in building which are burning, prevent these fires altogether, or other tactics. These programs will result in less death or injury due to fire, which is an obvious health benefit. 

Car seats also have proven effects on increasing the safety of children and infants during collision. It stands to reason that increased car seat installation will result in less injury to children during collision, which will make them healthier. 

What about the other two? Recycling can have an important health effect by decreasing the amount of garbage that ends up in a landfill! Consider this: would you live next to a landfill? Why not? Garbage going to landfills isn't good for air quality and can affect water quality as well--through leakage from landfills or trash ending up in waterways directly. It stands to reason that the more recycling there is, the less trash there may be. Less trash means less pollution. Less pollution means better air and water quality. Therefore, recycling can have an important effect on a community's health. 

However, as beneficial as they may be, cultural festivals may have the least positive health benefits. Certainly, feeling prideful in oneself may encourage better health and self esteem, but that may not alway be the case. It depends on the culture, for example. What if this cultural festival revolves around espousing hate and drinking twinkie and soda smoothies? While this is an obviously ridiculous example, there are cultures that exist that most may not consider the healthiest. Secondly, these festivals may only happen every once in a while. Even if they were to be beneficial, they may not have a lasting affect on the community. The benefits you may see might only be temporary. Therefore, this last option would be the least likely to promote community health on a wide scale.