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 16
Blue 13
Green 13
Yellow 20
Purple 8
If the spinner is spun 500 more times, about how many times would you expect to land on purple? Round your answer to the nearest whole number.

Spinner Results
Color Frequency
Red 16
Blue 13
Green 13
Yellow 20
Purple 8
If the spinner is spun 500 more times, about how many times would you expect to land on purple? Round your answer to the nearest whole number.

1 answer

To find the expected frequency of landing on purple if the spinner is spun 500 more times, we first need to calculate the probability of landing on purple based on the current results.

The total number of spins recorded so far is 16 + 13 + 13 + 20 + 8 = 70.

The probability of landing on purple based on the current results is 8/70 = 0.1143.

If the spinner is spun 500 more times, we can expect that about 0.1143 of those spins will result in landing on purple:

0.1143 * 500 = 57.15

Rounded to the nearest whole number, we would expect to land on purple about 57 times if the spinner is spun 500 more times.