Modern assembly relies on parts built to specifications (spec) so that the components fit together to make the whole. An appliance requires two components, Type A and Type B, supplied by different manufacturers. A robot randomly selects a component from a batch of Type A components and a second component from a batch of Type B components. The appliance works only if both components are within specifications. It is known that 5% of Type A components and 10% of Type B components are out of specifications.
(a) What is the probability that the appliance produced by the robot selecting one component from each batch at random works? State any assumptions clearly.
(b) The robot tests the appliance as it is assembled. It discovers that the current applicance does not work because the parts are not compatible. What is the probability that component that is out of spec is the Type A component?
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