Question

5) 15 points, 5 each. Provide a reasonable description (e.g. S -...]) of the sample space for the following random experiments. Define the events included for each experiment: a) Each of 4 bridges on a highway corridor is analyzed and then classified as above or below specification. (4 points) b) In a simple game of darts, 3 darts are thrown at a board and can land in the center section or outer section of the board. (4 points) c) In a potato chip manufacturing plant the quality control engineer draws a chip at random and classifies it as high quality or mediocre, and also as large, medium or small in size. (4 points)

Answer 1

a. There are 4 bridges on a highway corridor.

Therefore sample space S ={B₁,B₂,B₃,B₄ }

Let A be the event that the bridge is above specifications.

Let B be the event that the bridge is below specifications.

b. There are 3 darts thrown at a board.

Therefore sample space S ={D₁,D₂,D₃}

Let A be the event that the dart land in the center section of the board .

Let B be the event that the dart land in the outer section of the board.

c. Let there are n number of chips.

Therefore sample space S ={C₁,C₂,C₃,..............,C_n}

Let A be the event that the chip selected is of high quality.

Let B be the event that the chip selected is mediocre.

Let C be the event that the chip selected is of large size.

Let D be the event that the chip selected is of medium size.

Let E be the event that the chip selected is of small size.