Events A, B and C given below contain possible values for the soil bearing capac

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Events A, B and C given below contain possible values for the soil bearing capacities (strengths) (kN/m2 ) of three adjacent sites. A = {100, 120, 150, 170} B = {120, 130, 140} C = {130, 135} a. Determine the sample points in the intersection of A and B and in the union of A and B. b. Determine the sample points in the intersection of B and C and in the union of B and C. c. Among the events A, B and C, which two are mutually exclusive (ME)? d. Determine the sample points in the union of A, B and C. 2. Kiewit Construction Company, http://www.kiewit.com/, is currently bidding for two jobs. Kiewit can either win or lose these jobs. a. Identify all possible events (sample points) b. Identify the sample points for the following events: A = {Kiewit wins only one job} B = {Kiewit does not win any job} C = {Kiewit wins at least one job} c. Identify sample points in {AB} d. Identify sample points in {AB} 3. A CE3010 Geo-wall team performs tests on three different Geo-wall designs. The walls are tested to failure. D = Event {Wall can sustain a vertical surcharge load of 50 lbs. or more} i = Designed wall number = 1, 2, 3 a. Draw and shade the Venn diagram and write the event D = {Event that at least one designed wall can hold a surcharge load of 50 lbs. or more} b. Draw and shade the Venn diagram and write the event D = Event {the entire three designed wall can hold a surcharge load of 50 lbs. or more} c. Draw and shade the Venn diagram and write the event D = {only the first designed wall can hold a surcharge load of 50 lbs. or more} d. Draw and shade the Venn diagram and write the event D = {Exactly one designed wall can hold a surcharge load of 50 lbs. or more} e. Draw and shade the Venn diagram and writer the event D ={Either only the first designed wall or only both of the other designed walls can hold a surcharge load of 50 lbs. or more} f. Draw and shade the Venn diagram and writer the event D = {None of the designed walls can hold a surcharge load of 50 lbs. or more} Events A, B and C given below contain possible values for the soil bearing capacities (strengths) (kN/m2 ) of three adjacent sites. A = {100, 120, 150, 170} B = {120, 130, 140} C = {130, 135} a. Determine the sample points in the intersection of A and B and in the union of A and B. b. Determine the sample points in the intersection of B and C and in the union of B and C. c. Among the events A, B and C, which two are mutually exclusive (ME)? d. Determine the sample points in the union of A, B and C. 2. Kiewit Construction Company, http://www.kiewit.com/, is currently bidding for two jobs. Kiewit can either win or lose these jobs. a. Identify all possible events (sample points) b. Identify the sample points for the following events: A = {Kiewit wins only one job} B = {Kiewit does not win any job} C = {Kiewit wins at least one job} c. Identify sample points in {AB} d. Identify sample points in {AB} 3. A CE3010 Geo-wall team performs tests on three different Geo-wall designs. The walls are tested to failure. D = Event {Wall can sustain a vertical surcharge load of 50 lbs. or more} i = Designed wall number = 1, 2, 3 a. Draw and shade the Venn diagram and write the event D = {Event that at least one designed wall can hold a surcharge load of 50 lbs. or more} b. Draw and shade the Venn diagram and write the event D = Event {the entire three designed wall can hold a surcharge load of 50 lbs. or more} c. Draw and shade the Venn diagram and write the event D = {only the first designed wall can hold a surcharge load of 50 lbs. or more} d. Draw and shade the Venn diagram and write the event D = {Exactly one designed wall can hold a surcharge load of 50 lbs. or more} e. Draw and shade the Venn diagram and writer the event D ={Either only the first designed wall or only both of the other designed walls can hold a surcharge load of 50 lbs. or more} f. Draw and shade the Venn diagram and writer the event D = {None of the designed walls can hold a surcharge load of 50 lbs. or more} Events A, B and C given below contain possible values for the soil bearing capacities (strengths) (kN/m2 ) of three adjacent sites. A = {100, 120, 150, 170} B = {120, 130, 140} C = {130, 135} a. Determine the sample points in the intersection of A and B and in the union of A and B. b. Determine the sample points in the intersection of B and C and in the union of B and C. c. Among the events A, B and C, which two are mutually exclusive (ME)? d. Determine the sample points in the union of A, B and C. 2. Kiewit Construction Company, http://www.kiewit.com/, is currently bidding for two jobs. Kiewit can either win or lose these jobs. a. Identify all possible events (sample points) b. Identify the sample points for the following events: A = {Kiewit wins only one job} B = {Kiewit does not win any job} C = {Kiewit wins at least one job} c. Identify sample points in {AB} d. Identify sample points in {AB} 3. A CE3010 Geo-wall team performs tests on three different Geo-wall designs. The walls are tested to failure. D = Event {Wall can sustain a vertical surcharge load of 50 lbs. or more} i = Designed wall number = 1, 2, 3 a. Draw and shade the Venn diagram and write the event D = {Event that at least one designed wall can hold a surcharge load of 50 lbs. or more} b. Draw and shade the Venn diagram and write the event D = Event {the entire three designed wall can hold a surcharge load of 50 lbs. or more} c. Draw and shade the Venn diagram and write the event D = {only the first designed wall can hold a surcharge load of 50 lbs. or more} d. Draw and shade the Venn diagram and write the event D = {Exactly one designed wall can hold a surcharge load of 50 lbs. or more} e. Draw and shade the Venn diagram and writer the event D ={Either only the first designed wall or only both of the other designed walls can hold a surcharge load of 50 lbs. or more} f. Draw and shade the Venn diagram and writer the event D = {None of the designed walls can hold a surcharge load of 50 lbs. or more}

Explanation / Answer

1. (a) A intersection B={120}

A union B = {100,120,150,170,130,140}

(b) B intersection C = {130}

B union C ={ 120,130,140,135}

(c) C and A

(d) Union of ABC ={ 100,120,150,170,130,140,135}

2. Let the event of win and loss be represented as W and L respectively.

(a) K={ WW, WL, LW, LL}

(b) A= { WL,LW}

B = {LL}

C= {WW, WL, LW}

(c) A intersection B = null set ( no events)

(d) A union B = { WL,LW,LL}

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