Probability of Success (PoS) is a decision metric that has been widely used in drug development. Unlike the conventional statistical power, PoS accounts for both the assumed treatment effect and the uncertainty in its estimation from earlier studies. In the literature, closed-form expressions have been published for calculating PoS of a single phase 3 study using phase 2 data where the phase 2 and 3 studies have the same or different primary endpoints. When the phase 2 and 3 studies have different primary endpoints, a prior is specified for the correlation between endpoints to reflect the information known about the correlation before the start of phase 2. A closed-form expression for calculating joint PoS of multiple phase 3 studies has also been published in the literature. For more complex scenarios, e.g., when the phase 3 study itself has multiple primary endpoints, the PoS has typically been estimated via simulations because a closed-form expression is not available. Herein we provide a general analytical framework for deriving PoS. Using this framework, the PoS can be mathematically derived for all above scenarios. The analytical results are confirmed in a simulation study.