Problem 6. An oil production system has three major components, Alpha :1, Beta ,8 and Gamma y. The three components can have unexpected shutdowns due to mechanical or other reasons. The ratio of shutdown days to the total calendar days (365 days per year) is called downtime. Their downtime fractions are 3%, 4% and 5%, respectively. In order to produce oil and gas, the three components must be all operational. Assume that shutdowns of the three components are random and independent of each other. Let's define event A as \"Component Alpha is not operating\