Question

a jar contains 36 disks: 9 each of four colors-red, green, blue, and yellow. each set of disks of the same color is numbered from 1 to 9. suppose you draw one disk at random from the jar. define events b: get a blue disk, and e: get a disk with the number 8.
(a) make a two - way table that describes the sample space in terms of events b and e.

Explanation:

Step1: Determine the number of blue disks

Since there are 9 disks of each color and there are 4 colors (red, green, blue, yellow), the number of blue disks \( B = 9 \).

Step2: Determine the number of non - blue disks

The total number of disks \( N=36 \). The number of non - blue disks \(=36 - 9=27\).

Step3: Determine the number of blue disks with number 8

There is 1 disk with number 8 in each color. So the number of blue disks with number 8 \(=1\).

Step4: Determine the number of blue disks without number 8

The number of blue disks without number 8 \(=9 - 1=8\).

Step5: Determine the number of non - blue disks with number 8

Since there are 4 colors, the number of non - blue disks with number 8 \(=3\) (from red, green and yellow).

Step6: Determine the number of non - blue disks without number 8

The number of non - blue disks without number 8 \(=27- 3=24\).

Answer:

Color	Disk Number 8	Disk Not Number 8	Total
Not Blue	\(3\)	\(24\)	\(27\)
Total	\(4\)	\(32\)	\(36\)