Question

A drama teacher randomly assigns ten students different tasks in the school play: lighting, sound, and scene changes.

Josh creates a simulation to determine the probability of being randomly assigned to lighting. He places 10 colored tiles in a bag, where each color represents a different task.

For each trial, he draws one tile, records the color, and replaces the tile. The results of 150 trials are shown in the table.

Role Number of Draws
Lighting (Blue) 30
Sound (Green) 75
Scene Changes (Red) 45

Based on the results of Josh's simulation, determine the number of blue (B), green (G), and red (R) tiles that are most likely in the bag. Drag 10 colored tiles to the correct section of the bag.

Then, determine the probability that Josh will be randomly assigned to lighting.

The probability of josh being assigned to lighting is _______

Answer 1

20%

Explanation:

Based on the results of Josh's simulation, the most likely number of blue, green, and red tiles in the bag can be estimated by calculating the proportions of each color in the sample.

The total number of draws is 150, so the proportion of blue tiles is 30/150 = 0.2, the proportion of green tiles is 75/150 = 0.5, and the proportion of red tiles is 45/150 = 0.3.

To estimate the number of tiles of each color in the bag, we can assume that the sample proportions are approximately equal to the population proportions. Therefore, we can multiply each proportion by 10 to get an estimate of the number of tiles of each color in the bag.

The estimated number of blue tiles is 0.2 x 10 = 2, the estimated number of green tiles is 0.5 x 10 = 5, and the estimated number of red tiles is 0.3 x 10 = 3.

Therefore, the bag is most likely to contain 2 blue tiles, 5 green tiles, and 3 red tiles.

The probability that Josh will be randomly assigned to lighting (i.e., draw a blue tile) is the number of blue tiles divided by the total number of tiles in the bag, which is 2/10 = 0.2 or 20%.