Evildoer's plot-Part 2Discrete Mathematics Level 2
Surprisingly, all of the 10 superheroes from Evildoer's plot survived. But now, the evildoer has created a new game that the heroes have to do a fight to the death against their archenemy. There is a 100 percent chance that the first superhero that battles will have their archenemy knows their weakness and can use it to their advantage. The second archenemy has a 0 percent chance of knowing their weakness, the the third archenemy will have a 100 percent chance, and so on. What is the chance that all superheroes will live through the fight? Round your answer to the nearest ten-thousandth. Put you answer as a percent.
Details and assumptions:
1: All superheroes will have balanced out powers, and all have an equal chance of surviving if the villain does not know their weakness.
2: If the villain knows their weakness, they have a 25 percent chance of surviving. If the villain doesn't know their weakness, then they have a 50 percent chance of living.