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Sagot :
To tackle this problem, we'll separate it into our two main tasks: calculating the theoretical probability and the experimental probability of pulling a green marble from the bag.
### Theoretical Probability
The theoretical probability is based on the assumption that each marble has an equal chance of being selected.
1. Count the total number of marbles:
- Brown: 10
- Black: 10
- Green: 10
- Gold: 10
Total number of marbles = 10 + 10 + 10 + 10 = 40
2. Find the probability of pulling a green marble:
- There are 10 green marbles out of a total of 40 marbles.
Theoretical Probability [tex]\( P(\text{green}) = \frac{\text{Number of green marbles}}{\text{Total number of marbles}} = \frac{10}{40} = \frac{1}{4} \)[/tex]
3. Convert this into a percentage:
- [tex]\( P(\text{green}) \)[/tex] = [tex]\( \frac{1}{4} \times 100\% = 25\% \)[/tex]
### Experimental Probability
The experimental probability is determined by the results of the actual experiment.
1. Total number of trials:
- According to the table, the number of times each marble was pulled was recorded over 40 trials.
2. Find the frequency of pulling a green marble:
- The table shows that green marbles were pulled 7 times.
3. Calculate the experimental probability:
- Experimental Probability [tex]\( P(\text{green}) = \frac{\text{Frequency of green marbles}}{\text{Total number of trials}} = \frac{7}{40} \)[/tex]
4. Convert this into a percentage:
- [tex]\( P(\text{green}) = \frac{7}{40} \times 100\% = 17.5\% \)[/tex]
### Conclusion
- The theoretical probability of pulling a green marble is 25%.
- The experimental probability of pulling a green marble, based on 40 trials, is 17.5%.
Given this information, you can compare the solutions provided:
1. The theoretical probability, P(green), is [tex]\( 50\% \)[/tex] and the experimental probability is [tex]\( 115\% \)[/tex].
2. The theoretical probability, P(green), is [tex]\( 25\% \)[/tex] and the experimental probability is [tex]\( 25\% \)[/tex].
3. The theoretical probability, P(green), is [tex]\( 25\% \)[/tex] and the experimental probability is [tex]\( 175\% \)[/tex].
4. The theoretical probability, P(green), is [tex]\( 50\% \)[/tex] and the experimental probability is [tex]\( 7.0\% \)[/tex].
The correct statement is:
"The theoretical probability, P(green), is [tex]\( 25\% \)[/tex] and the experimental probability is [tex]\( 17.5\% \)[/tex]."
### Theoretical Probability
The theoretical probability is based on the assumption that each marble has an equal chance of being selected.
1. Count the total number of marbles:
- Brown: 10
- Black: 10
- Green: 10
- Gold: 10
Total number of marbles = 10 + 10 + 10 + 10 = 40
2. Find the probability of pulling a green marble:
- There are 10 green marbles out of a total of 40 marbles.
Theoretical Probability [tex]\( P(\text{green}) = \frac{\text{Number of green marbles}}{\text{Total number of marbles}} = \frac{10}{40} = \frac{1}{4} \)[/tex]
3. Convert this into a percentage:
- [tex]\( P(\text{green}) \)[/tex] = [tex]\( \frac{1}{4} \times 100\% = 25\% \)[/tex]
### Experimental Probability
The experimental probability is determined by the results of the actual experiment.
1. Total number of trials:
- According to the table, the number of times each marble was pulled was recorded over 40 trials.
2. Find the frequency of pulling a green marble:
- The table shows that green marbles were pulled 7 times.
3. Calculate the experimental probability:
- Experimental Probability [tex]\( P(\text{green}) = \frac{\text{Frequency of green marbles}}{\text{Total number of trials}} = \frac{7}{40} \)[/tex]
4. Convert this into a percentage:
- [tex]\( P(\text{green}) = \frac{7}{40} \times 100\% = 17.5\% \)[/tex]
### Conclusion
- The theoretical probability of pulling a green marble is 25%.
- The experimental probability of pulling a green marble, based on 40 trials, is 17.5%.
Given this information, you can compare the solutions provided:
1. The theoretical probability, P(green), is [tex]\( 50\% \)[/tex] and the experimental probability is [tex]\( 115\% \)[/tex].
2. The theoretical probability, P(green), is [tex]\( 25\% \)[/tex] and the experimental probability is [tex]\( 25\% \)[/tex].
3. The theoretical probability, P(green), is [tex]\( 25\% \)[/tex] and the experimental probability is [tex]\( 175\% \)[/tex].
4. The theoretical probability, P(green), is [tex]\( 50\% \)[/tex] and the experimental probability is [tex]\( 7.0\% \)[/tex].
The correct statement is:
"The theoretical probability, P(green), is [tex]\( 25\% \)[/tex] and the experimental probability is [tex]\( 17.5\% \)[/tex]."
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