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.
1. What is the probability that a profitable game will be predicted and the game will actually fail?