An office complex is lit by lightbulbs made by 2 companies, with 60% of the bulbs in use made by company A and 40% by company B. The lifetime (in years) for the 2 companies' bulbs are continuous uniform random variables Ta and Tb, respectively. However, the companies produce bulbs of different reliability, with 4<= Ta <= 9 and 2<=Tb <= 12
a) What is the probability that a lightbulb made by company A fails before 5 years of use, P(Ta< 5)?
b) If a lightbulb in an office fails exactly after 5 years of use, what is the probability that it was made by company A, P(A|T =5)?