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Unformatted text preview: 47 CHAPTER 2 Section 2.1 1. a. S = { 1324, 1342, 1423, 1432, 2314, 2341, 2413, 2431, 3124, 3142, 4123, 4132, 3214, 3241, 4213, 4231 } b. Event A contains the outcomes where 1 is first in the list: A = { 1324, 1342, 1423, 1432 } c. Event B contains the outcomes where 2 is first or second: B = { 2314, 2341, 2413, 2431, 3214, 3241, 4213, 4231 } d. The compound event A ∪ B contains the outcomes in A or B or both: A ∪ B = {1324, 1342, 1423, 1432, 2314, 2341, 2413, 2431, 3214, 3241, 4213, 4231 } 2. a. Event A = { RRR, LLL, SSS } b. Event B = { RLS, RSL, LRS, LSR, SRL, SLR } c. Event C = { RRL, RRS, RLR, RSR, LRR, SRR } d. Event D = { RRL, RRS, RLR, RSR, LRR, SRR, LLR, LLS, LRL, LSL, RLL, SLL, SSR, SSL, SRS, SLS, RSS, LSS } e. Event D ′ contains outcomes where all cars go the same direction, or they all go different directions: D ′ = { RRR, LLL, SSS, RLS, RSL, LRS, LSR, SRL, SLR } Because Event D totally encloses Event C, the compound event C ∪ D = D: C ∪ D = { RRL, RRS, RLR, RSR, LRR, SRR, LLR, LLS, LRL, LSL, RLL, SLL, SSR, SSL, SRS, SLS, RSS, LSS } Using similar reasoning, we see that the compound event C ∩ D = C: C ∩ D = { RRL, RRS, RLR, RSR, LRR, SRR } Chapter 2: Probability 48 3. a. Event A = { SSF, SFS, FSS } b. Event B = { SSS, SSF, SFS, FSS } c. For Event C, 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 2 nd and 3 rd positions: Event C = { SSS, SSF, SFS } d. Event C ′ = { SFF, FSS, FSF, FFS, FFF } Event A ∪ C = { SSS, SSF, SFS, FSS } Event A ∩ C = { SSF, SFS } Event B ∪ C = { SSS, SSF, SFS, FSS } Event B ∩ C = { SSS SSF, SFS } 4. a. 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 c. Outcome numbers 1, 16 d. Outcome numbers 1, 2, 3, 5, 9 e. In words, the UNION described is the event that either all of the mortgages are variable, or that at most all of them are variable: outcomes 1,2,3,5,9,16. The INTERSECTION described is the event that all of the mortgages are fixed: outcome 1. f. The UNION described is the event that either exactly three are fixed, or that all four are the same: outcomes 1, 2, 3, 5, 9, 16. The INTERSECTION in words is the event that exactly three are fixed AND that all four are the same. This cannot happen. (There are no outcomes in common) : b ∩ c = ∅ . Chapter 2: Probability 49 5. a. Outcome Number Outcome 1 111 2 112 3 113 4 121 5 122 6 123 7 131 8 132 9 133 10 211 11 212 12 213 13 221 14 222 15 223 16 231 17 232 18 233 19 311 20 312 21 313 22 321 23 322 24 323 25 331 26 332 27 333 b. Outcome Numbers 1, 14, 27 c. Outcome Numbers 6, 8, 12, 16, 20, 22 d. Outcome Numbers 1, 3, 7, 9, 19, 21, 25, 27 Chapter 2: Probability 50 6....
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 Spring '07
 Parzen
 Conditional Probability, Probability, Probability theory, Pallavolo Modena, Sisley Volley Treviso

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