Continuous uniform random variables

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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)?

Reference no: EM131087349

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