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 me- chanical 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. Calculate the following:

(a) PLX-5-3,Z-2)

(b) P(X = 8)

(c) PLX 8Y 1)

(d) P(X8Y=1)

(c) P(X = 7,Y=1|Z=2)