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A spinner is divided into five colored sections that are not of equal size: ed, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below:

Spinner Results

Color
Frequency

Red
2

Blue
10

Green
3

Yellow
4

Purple
20

If the spinner is spun 1300 more times, about how many times would you expect to land on yellow? Round your answer to the nearest whole number.

A spinner is divided into five colored sections that are not of equal size: ed, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below: $\newline$ \begin{tabular}{|c|c|} $\newline$ \hline Spinner Results \\ $\newline$ \hline Color & Frequency \\ $\newline$ \hline Red & $2$ \\ $\newline$ \hline Blue & $10$ \\ $\newline$ \hline Green & $3$ \\ $\newline$ \hline Yellow & $4$ \\ $\newline$ \hline Purple & $20$ \\ $\newline$ \hline $\newline$ \end{tabular} $\newline$ If the spinner is spun $1300$ more times, about how many times would you expect to land on yellow? Round your answer to the nearest whole number.

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Full solution

Q. A spinner is divided into five colored sections that are not of equal size: ed, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below:

\newline

\begin{tabular}{|c|c|}

\newline

\hline Spinner Results \\

\newline

\hline Color & Frequency \\

\newline

\hline Red &

2

\\

\newline

\hline Blue &

10

\\

\newline

\hline Green &

3

\\

\newline

\hline Yellow &

4

\\

\newline

\hline Purple &

20

\\

\newline

\hline

\newline

\end{tabular}

\newline

If the spinner is spun

1300

more times, about how many times would you expect to land on yellow? Round your answer to the nearest whole number.

Calculate total spins: Calculate the total number of spins recorded. $\newline$ Total spins = $\text{Frequency(Red)} + \text{Frequency(Blue)} + \text{Frequency(Green)} + \text{Frequency(Yellow)} + \text{Frequency(Purple)}$ $\newline$ Total spins = $2 + 10 + 3 + 4 + 20$ $\newline$ Total spins = $39$
Calculate probability of yellow: Calculate the probability of landing on yellow. $\text{Probability}(\text{Yellow}) = \frac{\text{Frequency}(\text{Yellow})}{\text{Total spins}}$ $\text{Probability}(\text{Yellow}) = \frac{4}{39}$
Estimate expected frequency: Use the probability to estimate the expected frequency of landing on yellow in $1300$ additional spins. $\newline$ Expected frequency(Yellow) = Probability(Yellow) $\times$ Additional spins $\newline$ Expected frequency(Yellow) = $(4 / 39) \times 1300$ $\newline$ Expected frequency(Yellow) $\approx 133.33$
Round expected frequency: Round the expected frequency to the nearest whole number. $\newline$ Expected frequency( $\text{Yellow}$ ) rounded = $133$ (to the nearest whole number)

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