A manufactured device has exactly one of three mutually exclusive fault types: electrical, mechanical or other. Their probabilities are xxx, 2x 2x\,2x and 1−3x1-3x1−3x respectively. In a batch of 200 devices, the expected number with an electrical fault is 48.
Find the probability of each fault type.
Two devices are selected independently. Find the probability that they have the same fault type.
Find the probability that at least one of the two devices has an electrical fault.