Test results from an electronic circuit board indicate that 50% of board failures are caused by assembly defects, 30% are due to electrical components, and 20% are due to mechanical defects. Suppose that 10 boards fail independently. Let the random variables X, Y, and Z denote the number of assembly, electrical, and mechanical defects among the 10 boards.
(a) P(X = 5, Y = 3, Z = 2)
(b) P(X = 8)
(c) P(X = 8 | Y = 1)
(d) P(X ? 8 | Y = 1)
(e) P(X = 7, Y = 1 | Z = 2)