Problem 1: Dead Pan, a video game developer, has a 70% chance of developing a profitable video game.

Problem 1:

Dead Pan, a video game developer, has a 70% chance of developing a profitable video game. The company's management is considering a new game and assesses the probability of developing a profitable game based on market research. In the past, 90% of their profitable games had been correctly predicted to be profitable by market research. At the same time, 20% of their failed games had also been predicted to be profitable by market research. What is the probability that a profitable game will be predicted and the game will actually fail?

Problem 2:

Market Researchers Inc has hired a project consulting firm to perform a study to determine if a project to be embarked by this company will be successful or it will fail. In similar studies performed by past market researchers, the market research study indicated that the project will be successful 85% of the time. On the other hand, whenever the project actually fails, the market study incorrectly predicted that the project will be successful; 20% of the time. Before the study was performed, it believed there is 70% chance that the project will be successful. When Market Researches Inc performs the study for this project the results predicts it will be successful. Given the results of this study, what is the probability that the project will actually be successful