A dance studio teaches students a contemporary dance form. It is observed that the probability of students from this studio becoming dance teachers is $0\mathrm{.}69.$ An event management company wants to use this studio for a show. They decide to observe it for a year before making the deal. They enroll $120$ students of their own in this studio and decide that once $75$ of them get jobs as dance teachers, they will sign the contract with them. What is the probability that the event management company will sign the contract with the dance studio?