Question

Spinner Results
Color Frequency
Red 5
Blue 6
Green 6
Yellow 19
Purple 12
Based on these results, express the probability that the next spin will land on red or green or yellow as a decimal to the nearest hundredth.

Answer 1

To calculate the probability that the next spin will land on red, green, or yellow, we first need to find the total number of spins.

We do this by summing the frequencies of each color:

\[
\text{Total Spins} = 5 \text{ (Red)} + 6 \text{ (Blue)} + 6 \text{ (Green)} + 19 \text{ (Yellow)} + 12 \text{ (Purple)} = 48
\]

Next, we find the total frequency of the colors we are interested in (red, green, and yellow):

\[
\text{Favorable Outcomes} = 5 \text{ (Red)} + 6 \text{ (Green)} + 19 \text{ (Yellow)} = 30
\]

Now, we calculate the probability \( P \) that the next spin will land on red, green, or yellow:

\[
P(\text{Red or Green or Yellow}) = \frac{\text{Favorable Outcomes}}{\text{Total Spins}} = \frac{30}{48}
\]

Now, we simplify the fraction:

\[
\frac{30}{48} = \frac{5}{8}
\]

Next, we convert this fraction to a decimal:

\[
\frac{5}{8} = 0.625
\]

Finally, we round the result to the nearest hundredth:

\[
0.625 \approx 0.63
\]

Therefore, the probability that the next spin will land on red or green or yellow is

\[
\boxed{0.63}
\]