PLEASE ANSWER THE QUESTION IF YOU ARE SURE ABOUT THE ANSWER IS CORRECT! THANK YO

Question

PLEASE ANSWER THE QUESTION IF YOU ARE SURE ABOUT THE ANSWER IS CORRECT! THANK YOU IN ADVANCE.

Describe (e.g. S ={…}) the sample space for the following random experiments.

Define the events included for each experiment:

a) You have to analyze 4 bridges on a highway corridor in order and classify each as requiring or not

requiring maintenance. (4 points)

b) In a simple game of darts, 4 darts are thrown at a board and can land in the center section or outer

section of the board. (4 points)

c) You want to book your next vacation and do some research. After, you classify the option as high cost

and medium costs, as well as long distance, medium distance, and short distance from Davis (4 points)

Explanation / Answer

(a) Let the bridges be B1,B2,B3 and B4 and Let Y denote yes, requires Maintenance and N denote No, does not require maintenance. The sample space is as follows:

Therefore the sample space is (N,N,N,N), (N,N,N,Y), (N,N,Y,N), (N,Y,N,N), (Y,N,N,N), (N,N,Y,Y), (Y,Y,N,N), (Y,N,N,Y),(N,Y,Y,N), (Y,N,Y,N), (N,Y,N,Y), (Y,Y,Y,N), (Y,Y,N,Y), (Y,N,Y,Y), (N,Y,Y,Y), (Y,Y,Y,Y)

(b) Let the darts be D1,D2,D3 AND D4. Let C denote the Center section and O denote the outer section. Just like in (a) we get 16 options, which are as follows:

Therefore the sample space is (C,C,C,C), (C,C,C,O), (C,C,O,C), (C,O,C,C), (O,C,C,C), (C,C,O,O), (O,O,C,C), (C,O,O,C), (O,C,C,O), (O,C,O,C), (C,O,C,O), (O,O,O,C), (O,O,C,O), (O,C,O,O), (C,O,O,O), (O,O,O,O)

(c) Let LD=Long distance, MD=Medium distance, SD=short distance, HC=High cost, MC=Medium cost

For every type of distance that we travel, we have 2 costs. Therefore the sample space is as folows

(LD,HC), (LD,MC), (MD,HC), (MD,MC), (SD,HC), (SD,MC),

B1 B2 B3 B4 1 N N N N 2 N N N Y 3 N N Y N 4 N Y N N 5 Y N N N 6 Y Y N N 7 N N Y Y 8 Y N N Y 9 N Y Y N 10 Y N Y N 11 N Y N Y 12 Y Y Y N 13 Y Y N Y 14 Y N Y Y 15 N Y Y Y 16 Y Y Y Y

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