Question

A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below:
Spinner Results
Color Frequency
Red 4
Blue 3
Green 2
Yellow 2
Purple 6
Based on these results, express the probability that the next spin will land on blue as a fraction in simplest form.

Answer 1

To find the probability that the next spin will land on blue, we can use the frequency of the blue section and the total number of spins to calculate the probability.

First, let's calculate the total frequency of all the spins:

\[
\text{Total frequency} = \text{Red} + \text{Blue} + \text{Green} + \text{Yellow} + \text{Purple} = 4 + 3 + 2 + 2 + 6
\]

Calculating that gives:

\[
\text{Total frequency} = 4 + 3 + 2 + 2 + 6 = 17
\]

Next, we look at the frequency for the color blue, which is given as 3.

Now, the probability \( P \) that the next spin will land on blue can be calculated using the formula:

\[
P(\text{Blue}) = \frac{\text{Frequency of Blue}}{\text{Total Frequency}} = \frac{3}{17}
\]

The fraction \( \frac{3}{17} \) is already in its simplest form.

Thus, the probability that the next spin will land on blue is:

\[
\boxed{\frac{3}{17}}
\]