# HW2.pdf - Probability and Statistics for Engineers...

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49 3. a. A = { SSF, SFS, FSS }. b. B = { SSS, SSF, SFS, FSS }. c. For event C to occur, the system must have component 1 working ( S in the first position), then at least one of the other two components must work (at least one S in the second and third positions): C = { SSS, SSF, SFS }. d. C = { SFF, FSS, FSF, FFS, FFF }. A C = { SSS, SSF, SFS, FSS }. A C = { SSF, SFS }. B C = { SSS, SSF, SFS, FSS }. Notice that B contains C , so B C = B . B C = { SSS SSF, SFS }. Since B contains C , B C = C. 4. a. The 2 4 = 16 possible outcomes have been numbered here for later reference. Home Mortgage Number Outcome 1 2 3 4 1 F F F F 2 F F F V 3 F F V F 4 F F V V 5 F V F F 6 F V F V 7 F V V F 8 F V V V 9 V F F F 10 V F F V 11 V F V F 12 V F V V 13 V V F F 14 V V F V 15 V V V F 16 V V V V b. Outcome numbers 2, 3, 5, 9 above. c. Outcome numbers 1, 16 above. d. Outcome numbers 1, 2, 3, 5, 9 above. e. In words, the union of (c) and (d) is the event that either all of the mortgages are variable, or that at most one of them is variable-rate: outcomes 1, 2, 3, 5, 9, 16. The intersection of (c) and (d) is the event that all of the mortgages are fixed-rate: outcome 1.

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