Question

you spin the spinner once. what is p(even or factor of 32)? write your answer as a percentage rounded to the nearest tenth.

Explanation:

Step1: List elements in each set

The numbers on the spinner are 2, 3, 4, 5, 6, 7, 8, 9.
Even - numbered set \(A=\{2,4,6,8\}\), factors of 32 set \(B = \{2,4,8\}\).

Step2: Use the formula for \(P(A\cup B)\)

The formula for \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\).
The total number of outcomes \(n = 8\).
\(P(A)=\frac{4}{8}\), \(P(B)=\frac{3}{8}\), \(P(A\cap B)=\frac{3}{8}\).

Step3: Calculate \(P(A\cup B)\)

\[

$$\begin{align*} P(A\cup B)&=\frac{4}{8}+\frac{3}{8}-\frac{3}{8}\\ &=\frac{4}{8}\\ & = 0.5 \end{align*}$$

\]

Step4: Convert to percentage

To convert 0.5 to a percentage, we multiply by 100. \(0.5\times100 = 50.0\%\)

Answer:

50.0%