There are many factors that affect the relationship between a person's major and his or her future success. Therefore, at best we could say that the relationship is unclear.
On the one hand, some jobs are in more demand than others. Also, some jobs lead to higher incomes than others. Therefore, it might be more likely for people in general to become very successful if they decide to become doctors than if they decide to become actors, for example.
However, there is also an element of talent and passion that needs to be considered. A person might become more successful being an actor than being a doctor if he truly has a passion for this area, or is very talented.
Finally, hard work plays a big part in future success. And people tend to work harder at things they are passionate about.
Therefore, the connection is not a straightforward one and there are many factors to keep in mind when studying this relationship.