To predict the number of times a green tile will be drawn from the bag, we first need to find out the probability of drawing a green tile in a single draw. This can be calculated by dividing the number of green tiles by the total number of tiles in the bag.
Let's calculate the total number of tiles in the bag:
- There are 3 blue tiles.
- There are 4 green tiles.
- There are 3 red tiles.
Therefore, the total number of tiles is:
3 (blue) + 4 (green) + 3 (red) = 10 tiles
Now, to find the probability of drawing a green tile in one draw, we take the number of green tiles and divide it by the total number of tiles:
Probability of drawing a green tile = Number of green tiles / Total number of tiles
So the probability is:
Probability of green = 4 (green) / 10 (total) = 0.4
Since the tile will be replaced after each draw, the probability of drawing a green tile remains the same for each of the 50 draws.
Now, to find the expected number of times a green tile will be drawn out of 50 draws, we multiply the probability by the number of trials (draws):
Expected number of draws of a green tile = Probability of green Number of trials
Expected draws of green = 0.4 50
Expected draws of green = 20
So, a reasonable prediction for the number of times a green tile will be drawn after 50 draws with replacement is 20 times.
