You randomly draw a marble from a bag of 320 marbles. You record its color and replace it. Use the results shown in the table to predict the number of marbles in the bag that are the given color. Blue:10 Green:8 Purple:2
If this is supposed to indicate the number of marbles directly, then out of every 20, 10 are blue, 8 are green and 2 are purple.
320/20 = 16
Multiply each value by 16.
To predict the number of marbles in the bag that are a given color, you need to know the total number of trials conducted and the proportion of each color that appeared in those trials.
From the information provided, we are given the following:
- Total marbles in the bag = 320
- Number of blue marbles drawn = 10
- Number of green marbles drawn = 8
- Number of purple marbles drawn = 2
To predict the number of marbles of a specific color in the bag, you can use the concept of proportions.
1. Calculate the proportion of each color based on the number of marbles drawn:
- Proportion of blue marbles = Number of blue marbles drawn / Total marbles drawn
- Proportion of green marbles = Number of green marbles drawn / Total marbles drawn
- Proportion of purple marbles = Number of purple marbles drawn / Total marbles drawn
2. Multiply the proportions obtained in step 1 by the total number of marbles in the bag to get the predicted number of marbles of each color:
- Predicted number of blue marbles = Proportion of blue marbles * Total marbles in the bag
- Predicted number of green marbles = Proportion of green marbles * Total marbles in the bag
- Predicted number of purple marbles = Proportion of purple marbles * Total marbles in the bag
Let's calculate the predictions:
1. Calculate the proportions:
- Proportion of blue marbles = 10 / (10 + 8 + 2) = 10 / 20 = 0.5
- Proportion of green marbles = 8 / (10 + 8 + 2) = 8 / 20 = 0.4
- Proportion of purple marbles = 2 / (10 + 8 + 2) = 2 / 20 = 0.1
2. Calculate the predictions:
- Predicted number of blue marbles = 0.5 * 320 = 160 marbles
- Predicted number of green marbles = 0.4 * 320 = 128 marbles
- Predicted number of purple marbles = 0.1 * 320 = 32 marbles
Therefore, based on the proportions obtained from the given results, the predicted number of marbles in the bag for each color is as follows:
- Blue: 160 marbles
- Green: 128 marbles
- Purple: 32 marbles
To predict the number of marbles in the bag that are of a given color, we can use the concept of probability.
The probability of an event is defined as the number of favorable outcomes divided by the total number of possible outcomes. In this case, the favorable outcome is drawing a marble of a specific color, and the total number of possible outcomes is the total number of marbles in the bag.
So, to predict the number of marbles of a specific color, we calculate the probability of drawing a marble of that color and multiply it by the total number of marbles in the bag.
For example, to predict the number of blue marbles in the bag:
1. Calculate the probability of drawing a blue marble:
Probability of drawing a blue marble = Number of blue marbles / Total number of marbles = 10 / 320 = 1/32
2. Multiply the probability by the total number of marbles in the bag:
Number of blue marbles = Probability of drawing a blue marble * Total number of marbles = (1/32) * 320 = 10
Therefore, the predicted number of blue marbles in the bag is 10.
Similarly, you can follow the same steps to predict the number of green and purple marbles using the given probabilities:
Number of green marbles = (Probability of drawing a green marble) * (Total number of marbles) = (8 / 320) * 320 = 8
Number of purple marbles = (Probability of drawing a purple marble) * (Total number of marbles) = (2 / 320) * 320 = 2
Therefore, the predicted numbers of green and purple marbles in the bag are 8 and 2, respectively.