Leah is flying from Boston to Denver with a connection in Chicago. The probability her first flight leaves on time is 0.15. If the flight is on time, the probability that her luggage will make the connecting flight in Chicago is 0.95, but if the first flight is delayed, the probability that the luggage will make it is only 0.65.
a) Are the first flight leaving on time and the luggage making the connection independent events? Explain.
b) What is the probability that her luggage arrives in Denver with her?