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 7
Blue 6
Green 12
Yellow 19
Purple 19
Based on these results, express the probability that the next spin will land on blue as a fraction in simplest form.

1 answer

To find the probability that the next spin will land on blue, we first need to determine the total number of spins.

We can do this by adding up the frequencies of all the colors:

\[ \text{Total Spins} = \text{Red} + \text{Blue} + \text{Green} + \text{Yellow} + \text{Purple} \]

Substituting the values from the table:

\[ \text{Total Spins} = 7 + 6 + 12 + 19 + 19 \]

Calculating this step-by-step:

\[ 7 + 6 = 13 \] \[ 13 + 12 = 25 \] \[ 25 + 19 = 44 \] \[ 44 + 19 = 63 \]

So, the total number of spins is 63.

Next, we determine the probability of landing on blue. The probability \( P(\text{Blue}) \) is given by the ratio of the number of times blue was landed on to the total number of spins.

\[ P(\text{Blue}) = \frac{\text{Frequency of Blue}}{\text{Total Spins}} = \frac{6}{63} \]

Now, we simplify \(\frac{6}{63}\).

To simplify the fraction, we find the greatest common divisor (GCD) of 6 and 63, which is 3.

Now we divide both the numerator and the denominator by their GCD:

\[ \frac{6 \div 3}{63 \div 3} = \frac{2}{21} \]

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

\[ \boxed{\frac{2}{21}}. \]