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Answer :
To solve the problem of estimating the probability that the next bottle is defective, we need to analyze the provided sequence: [tex]$00000000000000100000$[/tex].
Here's a step-by-step solution:
1. Count the Total Number of Bottles:
- Look at the sequence: [tex]$00000000000000100000$[/tex]
- Count each number in the sequence. There are 20 numbers in total.
2. Identify Defective Bottles:
- A defective bottle is marked with a '1'.
- In the sequence, identify how many '1's there are. There is only one '1' present.
3. Calculate the Probability of a Defective Bottle:
- The probability of an event is determined by dividing the number of successful outcomes by the total number of possible outcomes.
- In this case, the number of defective bottles (successful outcome, as per the problem context) is 1.
- Therefore, the probability that the next bottle is defective is calculated as:
[tex]\[
\text{Probability} = \frac{\text{Number of Defective Bottles}}{\text{Total Number of Bottles}} = \frac{1}{20}
\][/tex]
4. Conclusion:
- The estimated probability that the next bottle is defective is [tex]\(\frac{1}{20}\)[/tex].
Therefore, the correct answer is [tex]\(\frac{1}{20}\)[/tex].
Here's a step-by-step solution:
1. Count the Total Number of Bottles:
- Look at the sequence: [tex]$00000000000000100000$[/tex]
- Count each number in the sequence. There are 20 numbers in total.
2. Identify Defective Bottles:
- A defective bottle is marked with a '1'.
- In the sequence, identify how many '1's there are. There is only one '1' present.
3. Calculate the Probability of a Defective Bottle:
- The probability of an event is determined by dividing the number of successful outcomes by the total number of possible outcomes.
- In this case, the number of defective bottles (successful outcome, as per the problem context) is 1.
- Therefore, the probability that the next bottle is defective is calculated as:
[tex]\[
\text{Probability} = \frac{\text{Number of Defective Bottles}}{\text{Total Number of Bottles}} = \frac{1}{20}
\][/tex]
4. Conclusion:
- The estimated probability that the next bottle is defective is [tex]\(\frac{1}{20}\)[/tex].
Therefore, the correct answer is [tex]\(\frac{1}{20}\)[/tex].
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