Yasmin has a bag containing 165 colored beads. Her classmates take turns selecting one bead from the bag without looking, recording the color in the table, and replacing the bead. If the bag contained an equal number of each color of bead, for which color is the experimental probability closest to the theoretical probability?
Color Red Brown Orange Yellow
Number of Beads 10 15 17 13
In order to determine the theoretical probability for each color, we need to calculate the ratio of each color to the total number of beads in the bag.
The total number of beads is 10 + 15 + 17 + 13 = 55 beads.
The theoretical probability for each color is as follows:
- Red: 10/55 = 0.1818
- Brown: 15/55 = 0.2727
- Orange: 17/55 = 0.3091
- Yellow: 13/55 = 0.2364
Now, we need to calculate the experimental probability for each color based on the number of times each color was selected by Yasmin's classmates.
Let's assume that each color was selected as follows:
- Red: 10 times
- Brown: 15 times
- Orange: 17 times
- Yellow: 13 times
The experimental probability for each color is as follows:
- Red: 10/55 ≈ 0.1818
- Brown: 15/55 ≈ 0.2727
- Orange: 17/55 ≈ 0.3091
- Yellow: 13/55 ≈ 0.2364
From the calculations, it can be seen that the experimental probability closest to the theoretical probability would be for the color Orange.