Sir i am stuck for this question

3. (15 marks) Suppose the light bulbs in the market are supplied by two factories A and B. Bulbs from factory A work for over 5000 hours in 99% of cases, whereas bulbs from factory B work for over 5000 hours in 95% of cases. It is known that factory A supplies 40% of the total bulbs available in the market. Assume that A represents the event that a randomly purchased bulb is supplied by factory A, B is the event that a randomly purchased bulb is supplied by factory B, and C is the event that a bulb works for over 5000 hours. (a) Write down the following probabilities P(A), P(CIA), P(C| B). [3 marks] (b) Find the probability P(C). [3 marks] (c) Find the probability P(B C). [3 marks] (d) Find the probability P(A|C) where C is the complement of event C. [3 marks] (e) Are two events, A and C, independent? Please justify your answer. [3 marks]