Burger City is a large chain of fast-food restaurants specializing in gourmet hamburgers. A mathematical model is now used to predict the success of new restaurants based on location and demographic information for that area. In the past, 70% of all restaurants that were opened were successful. The mathematical model has been tested in the existing restaurants to determine how effective it is. For the restaurants that were successful, 90% of the time the model predicted they would be, while 10% of the time the model predicted a failure. For the restaurants that were not successful, when the mathematical model was applied, 20% of the time it incorrectly predicted a successful restaurant while 80% of the time it was accurate and predicted an unsuccessful restaurant. If the model is used on a new location and predicts the restaurant will be successful, what is the probability that it actually is successful?