Using the given probabilities and information:
1. Purple Marbles:
Given the probability: [tex]\( P(P) = \frac{37}{300} \)[/tex], we multiply by the total number of marbles, which is 3000. Therefore:
[tex]\[
3000 \cdot \frac{37}{300} = 370
\][/tex]
So, there are probably 370 purple marbles in the bag.
2. Red Marbles:
The question text implies the provided probability should be [tex]\( \frac{25}{100} = \frac{1}{4} \)[/tex].
Given [tex]\( P(R) = \frac{1}{4} \)[/tex], we multiply by the total number of marbles:
[tex]\[
3000 \cdot \frac{1}{4} = 750
\][/tex]
3. White Marbles:
Given the probability: [tex]\( P(W) = \frac{8}{25} \)[/tex], we multiply by the total number of marbles:
[tex]\[
3000 \cdot \frac{8}{25} = 960
\][/tex]
So, there are probably 960 white marbles in the bag.
4. Yellow Marbles:
Given the setup indicates the total is assumed to be 3000, we need to check the number:
Given numbers add up as [tex]\(430 + 370 + 600 + 960 + 640 = 3000\)[/tex]:
- Probabilities and number outcomes are clear given 640 yellow marbles as total balance.
- Probabilities and number outcomes balance to complete ratios, verify possible form check unity.
Using the data provided:
1. We have [tex]\( \checkmark\)[/tex] 3000 marbles.
2. The law stating close results if sample size large enough is the Law of Large Numbers [tex]\( \large Numbers \)[/tex].
3. Only way to know the number of each color is through conducting a census [tex]\( \text{census} \)[/tex].
