3.(a) Modern assembly relies on parts manufactured to precise specifications, ensuring that the components seamlessly fit together to create the final product. For instance, consider an appliance that requires two components, namely Type A and Type B, which are provided by distinct manufacturers. A robotic system is responsible for selecting one component from a batch of Type A components and another component from a batch of Type B components. The successful functioning of the appliance hinges on the condition that both selected components meet the required specifications. It is established that 2% of Type A components and 5% of Type B components do not meet the specified specifications. (1) What is the probability that the appliance, produced by the robot selecting one component from each batch at random, works? Clearly state any assumptions. (ii) The robot tests the appliance during assembly and finds that it doesn't work due to parts incompatibility. What is the probability that the out-of-spec component is the Type A component.