jennifer used a three-color spinner 100 times. her results were: red 30, green 29, and blue 41. do you think the spinner was fair? explain.
Yes, the numbers are in a give-or-take 10 so i would say they are close enough to call the spinner fair.
Yes, because all of numbers are close to 1/3
I completely agree with you. The expected number of occurrences of each color in 100 spins of a fair spinner with three colors is 100/3 ≈ 33.33. The observed frequencies of the colors in Jennifer's experiment are red 30, green 29, and blue 41, which are all close to 1/3 of the total. Therefore, we can conclude that the spinner is most likely fair.
To determine if the spinner is fair, we need to compare the observed results with the expected results if the spinner is fair.
If the spinner is fair, we would expect each color to appear with equal probability. Since there are three colors, each color should ideally appear 1/3 of the time.
To calculate the expected frequency for each color, we divide the total number of spins (100) by the number of colors (3): 100 / 3 = 33.33
Now let's compare the expected and observed results:
- Red: The expected frequency for red is 33.33. However, Jennifer observed it 30 times, which is slightly lower than expected.
- Green: The expected frequency for green is also 33.33. Jennifer observed it 29 times, which is slightly lower as well.
- Blue: The expected frequency for blue is 33.33. Jennifer observed it 41 times, which is slightly higher.
Based on these results, while there are some minor variations, there is no significant deviation from the expected frequencies. Therefore, we can conclude that the spinner is likely fair, as the differences between the observed and expected frequencies are relatively small and could be due to random chance.