what is the probability that a market inspector will discover greater than five violation of the public health code

Let the random variable $X$ represent the number of violations of the public health code.

The probability that a market inspector will discover greater than 5 violations of health code is, $p(X\gt5)=\displaystyle \sum^{\infin}_{x=6}p(x)$ . This is equivalent to $p(X\gt5)=1-p(x\le5)=1-\{p(0)+p(1)+p(2)+p(3)+p(4)+p(5)\}$