An Approach to Resolving Two Paradoxes in Probability Theory

A new mathematical expectation formula with some hypotheses, notions and propositions was given to get rid of the challenge of St. Petersburg paradox and Pascal＇s wager. Relevant results show that it is very effective to apply the model to solve the expected revenue problems containing random events with low probability but high revenue. This work also provides the probability theory with a more widely applied perspective in group decision-making.