A problem on probability involving binomial distribution

I'm trying to figure out the method required to solve this problem, so I stripped out the actual values to keep from getting a direct answer.

A random sample of n people who walk to work are chosen, what is the probability that at least r of them are injured, given that the probability of being injured while walking to work is p.

I don't know where to go. It feels like a binomial probability problem, but it covers a range of trials and not just one value exactly. My guess was to calculate $1-BinomCDF(n,p,r-1)$. Does this seem accurate? For example, if $n=15$, $r=7$, $p=0.5$.

I would have $1-BinomCDF(15,0.5,6)$ or

$$1-\sum _{i=1}^{6}{\textstyle (}\genfrac{}{}{0ex}{}{15}{i}{\textstyle )}{0.5}^{i}(1-0.5{)}^{15-i}.$$

I'm trying to figure out the method required to solve this problem, so I stripped out the actual values to keep from getting a direct answer.

A random sample of n people who walk to work are chosen, what is the probability that at least r of them are injured, given that the probability of being injured while walking to work is p.

I don't know where to go. It feels like a binomial probability problem, but it covers a range of trials and not just one value exactly. My guess was to calculate $1-BinomCDF(n,p,r-1)$. Does this seem accurate? For example, if $n=15$, $r=7$, $p=0.5$.

I would have $1-BinomCDF(15,0.5,6)$ or

$$1-\sum _{i=1}^{6}{\textstyle (}\genfrac{}{}{0ex}{}{15}{i}{\textstyle )}{0.5}^{i}(1-0.5{)}^{15-i}.$$