You fly from Philadelphia to San Francisco with a connection in Dallas. The probability that your flight from Philadelphia to Dallas arrives on time is 0.8. If you arrive on time, then the probability that your luggage makes the connection to San Francisco is 0.9. If you are delayed, then the probability that your luggage makes the connection with you is 0.5. In either case, you make the flight.
(a) What is the probability that your luggage is there to meet you in San Francisco?
(b) If your luggage is not there to meet you, what is the probability that you were late arriving in Dallas?