Let be a random variable with distribution . A success is when . Now repeat 15 times (each trial is independent), denoting the trial as .
(i.e. the probabilities of success) are constant with respect to . In other words, you have 15 independent trials, success is constant ( ), and you are asked what is the probability of at least 2 successes. This smells like a binomial distribution if you let be the number of successes.
You use the distribution only to calculate .