You will model a small bayesian network that represents the relationship between yellow fingers, smoking, cancer, radiation, solar flares, and using a microwave. In this model, smoking can cause yellow fingers and cancer. Solar flares and making microwave popcorn can cause radiation, and radiation can cause cancer as well. The prior probability of smoking P(S) is 0.3. The prior probability of solar flares P(F) is 0.8. The prior probability of using the microwave is P(M) is 0.9. The conditional probability table for radiation is: F M P(R) 0 0 0.1 0 l 0.2 1 0 0.4 1 l 0.3 The conditional probability table for cancer is: s R P(C) o o 0.1 o 1 0.2 1 o 0.2 1 1 0.5 The conditional probability table for yellow fingers is s P(Y) o 0.1 1 0.9 Answer the following questions: What is the prior probability of cancer? What is the probability of smoking given cancer? What is the probability of smoking given cancer and radiation? Are solar flares and using the microwave independent given cancer? What is the probability of cancer if you never use a microwave