Answer to Question #81791 in Statistics and Probability for SON

Question

According to the historical data gathered by an insurance company, the probability of a fire is 0.01. A manufacturer of fire alarms has determined through testing that a certain fire alarm has a 0.1 conditional probability to go off given that there is no fire, and a 0.2 conditional probability to remain silent given that there is a fire. The meaning of “go off” is that a fire alarm makes a loud sound or a bomb explodes.
Event A is that a fire breaks out.
Event B is that the fire alarm goes off.
(a) If you hear this fire alarm go off, what is the conditional probability that there is a fire? In
other words, what is P(A|B)?
(b) What is the conjunction probability, P(Bc ∩ Ac) ?