3. The auto industry suffered from the shortage of semiconductor chips during the pandemic. The cost to car manufacturers in lost revenues is estimated in tens of billions of dollars. The causes of the shortage was complex but the existence of only several manufacturers was one of them. A car manufacturer, TesGF that depended on a single manufacturer, ChipCo, in China is considering to start working with a second manufacturer, SAmChips, in South America. TesGF's logic is that, unless both chip manufacturers face disruptions in their operations at the same time, its supply will keep owing, knowing that both manufacturers have excess capacity under normal operating conditions. TesGF wants to test this hypothesis under a set of assumptions regarding supplier performances. In a given month, ChipCo and SAmChips are expected to face disruptions with 3% and 6% probabilities, respectively. TesGF thinks that the two manufacturers face disruptions independently due to their distant geographical locations. TesGF does not keep much inventory of chips and it will have to stop its operations when both chip manufacturers face disruptions in the same month. TesGF will be able to operate normally under all other scenarios. Use 0 and S to represent the events that ChipCo and SAmChip face disruption in a given month, respectively. (a) What is the probability that TesGF will stop operations in a given month? (b) What is the probability that exactly one of the suppliers faces a disruption in a given month? (c) Given that exactly one of the chip manufacturers faced a disruption, What is the probability that the disrupted supplier is ChipCo? (d) TesGF has found another chip manufacturer, KorChips, in S. Korea and thinks that it may be a better idea to pair ChipCo and KorChips as its suppliers rather than ChipCo and SAmChips. This belief is based on the fact that KorChips has a 4% disruption probability in a given month, in contrast with the 6% of SAmChips's. TesGF is not condent if the disruptions of ChipCo and KorChips are independent as they are in closer geographical proximity. Based on past data, TesGF calculated the probability that ChipCo faces disruption and KorChips does not face disruption in a given month as 2%. Are the disruptions faced by ChipCo and KorChips independent? Is using ChipCo and KorChips better than using ChipCo and SAmChips in terms of the probability of continuing the operations of TesGF normally in a given month