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.
(b) find p(b).
(round to 2 decimal places. leave your answer in decimal form.)

Explanation:

Step1: Recall the formula for probability

The probability formula is \(P(B)=\frac{n(B)}{n(S)}\), where \(n(B)\) is the number of elements in event \(B\) and \(n(S)\) is the number of elements in the sample space.

Step2: Identify \(n(B)\) and \(n(S)\) from the table

From the table, the total number of blue disks \(n(B)=9\) (sum of blue - numbered \(3\) and blue - not numbered \(6\)? Wait, no, looking at the table: total blue is \(9\) (from the row labeled "Blue" in the "Total" column). The total number of disks \(n(S) = 36\) (from the "Total" row and "Total" column).

Step3: Calculate \(P(B)\)

Substitute into the formula: \(P(B)=\frac{9}{36}\). Simplify \(\frac{9\div9}{36\div9}=\frac{1}{4}=0.25\)

Answer:

\(0.25\)