Two analysts are in a big argument about the expected return of a stock and the probability of a global pandemic. They agree that there are 4 possible states of the world, and that the return on the stock in each state is given as:

State Return

Boom 30%

Normal 10%

Bust -10%

Pandemic -60%

They also agree that a boom will happen with probability = 20% and that normal will happen 60% of the time. Their disagreement is over the relative probabilities of bust and pandemic. Finally someone comes in and yells THE EXPECTED RETURN ON THE STOCK IS 9.995% and they agree that its settled. What is the probability of the Pandemic state?