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Answer :
To estimate the probability that the next bottle is defective, we need to analyze the data provided by the company. The sequence given is:
`00000000000000100000`
In this sequence, each '0' represents a correctly produced bottle, and each '1' represents a defective bottle.
1. Count the defective bottles: First, we count how many '1's (defective bottles) are in the sequence. In this sequence, there is only 1 defective bottle.
2. Count the total number of bottles: Next, we determine the total number of bottles produced. By counting all the numbers in the sequence, we find that there are 21 bottles in total.
3. Calculate the probability: To find the probability that the next bottle is defective, we divide the number of defective bottles by the total number of bottles:
[tex]\[
\text{Probability of defective bottle} = \frac{\text{Number of defective bottles}}{\text{Total number of bottles}} = \frac{1}{21}
\][/tex]
This fraction simplifies to approximately 0.0476.
Therefore, the probability that the next bottle is defective is about 0.0476. If we express this probability as a fraction from the given options, it matches closely with [tex]\(\frac{1}{20}\)[/tex], which is approximately 0.05, the nearest available choice. Thus, the correct answer is:
[tex]\(\frac{1}{20}\)[/tex]
`00000000000000100000`
In this sequence, each '0' represents a correctly produced bottle, and each '1' represents a defective bottle.
1. Count the defective bottles: First, we count how many '1's (defective bottles) are in the sequence. In this sequence, there is only 1 defective bottle.
2. Count the total number of bottles: Next, we determine the total number of bottles produced. By counting all the numbers in the sequence, we find that there are 21 bottles in total.
3. Calculate the probability: To find the probability that the next bottle is defective, we divide the number of defective bottles by the total number of bottles:
[tex]\[
\text{Probability of defective bottle} = \frac{\text{Number of defective bottles}}{\text{Total number of bottles}} = \frac{1}{21}
\][/tex]
This fraction simplifies to approximately 0.0476.
Therefore, the probability that the next bottle is defective is about 0.0476. If we express this probability as a fraction from the given options, it matches closely with [tex]\(\frac{1}{20}\)[/tex], which is approximately 0.05, the nearest available choice. Thus, the correct answer is:
[tex]\(\frac{1}{20}\)[/tex]
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