Question

Daniel’s spinner is divided into 8 equal sections.

A spinner divided into 8 equal sections labeled gray, green, red, purple, gray, green, yellow, blue.

He plans to spin it 80 times. Which equation predicts the number of times that he could spin green?
P (green) = StartFraction 1 over 8 EndFraction (80)
P (green) = StartFraction 2 over 8 EndFraction (80)
P (green) = StartFraction 3 over 8 EndFraction (80)
P (green) = one-half (80)

Answer 1

To determine the correct equation predicting the number of times Daniel could spin green, you first need to find the probability of landing on green.

In the spinner, there are 8 equal sections labeled as follows:
- gray
- green
- red
- purple
- gray
- green
- yellow
- blue

From the list, you can see that there are 2 sections labeled green out of a total of 8 sections. Therefore, the probability \( P \) of spinning green is:

\[
P(\text{green}) = \frac{\text{Number of green sections}}{\text{Total sections}} = \frac{2}{8} = \frac{1}{4}
\]

Now, to predict the number of times he spins green in 80 spins, you multiply the probability of spinning green by the total number of spins:

\[
\text{Expected number of greens} = P(\text{green}) \times \text{Total spins} = \frac{2}{8} \times 80 = \frac{1}{4} \times 80
\]

The equation that correctly predicts the number of times Daniel could spin green is:

\[
P(\text{green}) = \frac{2}{8}(80)
\]

So, the correct answer is:
**P (green) = StartFraction 2 over 8 EndFraction (80)**.