Let g be a finite group. The probability of a random pair of elements in g are
said to be co-prime when the greatest common divisor of order x and y where x and y in
g, is equal to one. Meanwhile the co-prime graph of a group is defined as a graph whose
vertices are elements of g and two distinct vertices are adjacent if and only if the greatest
common divisor of order x and y is equal to one. In this paper, the co-prime probability
and its graphs such as the types and the properties of the graph are determined.