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Use the relative frequency (experimental probability) to guess the number of purple, red, white, and yellow marbles. Do not use any spaces in your answers. Use / for the fraction bar and * for multiplication.

1. [tex]\(P(P)=\frac{37}{30}\)[/tex], so there are probably [tex]\(3000 \cdot \frac{37}{300}=370\)[/tex] purple marbles in the bag.
2. [tex]\(P(R)=\frac{25}{8}\)[/tex], so there are probably [tex]\(600 \cdot \frac{8}{25}=600\)[/tex] red marbles in the bag.
3. [tex]\(P(W)=\frac{8}{25}\)[/tex], so there are probably [tex]\(1200 \cdot \frac{8}{25}=960\)[/tex] white marbles in the bag.
4. [tex]\(P(Y)=\frac{4}{25}\)[/tex], so there are probably [tex]\(4000 \cdot \frac{4}{25}=640\)[/tex] yellow marbles in the bag.

We can assume that there are 430 blue marbles, 370 purple marbles, 600 red marbles, 960 white marbles, and 640 yellow marbles.

How many marbles do we have in total?
Total marbles: [tex]\(\boxed{3000}\)[/tex]

What law states that if our sample size is large enough, our results should be close to the theoretical probability?
The Law of Large [tex]\(\boxed{Numbers}\)[/tex]

If we took another sample (conducted another experiment), do you think we would get the exact same results?
Click to view the answer.

What is the only way to know exactly how many of each color are in the bag?
We need to conduct a(n) [tex]\(\boxed{census}\)[/tex]



Answer :

GinnyAnswer
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].

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