Answer :
To find the probability that the next bottle is defective, we need to understand the pattern of how bottles are marked. Here’s how you can figure it out step by step:
1. Count the Total Number of Bottles:
The sequence provided is a series of numbers where each '0' represents a correct bottle and each '1' represents a defective bottle. Count all the numbers in the sequence. There are 21 numbers in total.
2. Count the Number of Defective Bottles:
In the sequence, count how many '1's appear. There is 1 defective bottle in this sequence.
3. Calculate the Probability:
The probability of an event is calculated as the number of favorable outcomes (defective bottles) divided by the total number of outcomes (total bottles).
So, the probability [tex]\( P \)[/tex] that the next bottle is defective is:
[tex]\[
P(\text{defective}) = \frac{\text{Number of defective bottles}}{\text{Total number of bottles}} = \frac{1}{21}
\][/tex]
4. Interpreting the Result:
The calculated probability is approximately 0.0476, which means there is about a 4.76% chance that the next bottle is defective.
Therefore, the probability that the next bottle will be defective is [tex]\(\frac{1}{21}\)[/tex]. This corresponds to approximately 0.0476, which is not exactly any option provided but closest to [tex]\(\frac{1}{20}\)[/tex] when considering typical rounding in percentage terms to two decimal places.
1. Count the Total Number of Bottles:
The sequence provided is a series of numbers where each '0' represents a correct bottle and each '1' represents a defective bottle. Count all the numbers in the sequence. There are 21 numbers in total.
2. Count the Number of Defective Bottles:
In the sequence, count how many '1's appear. There is 1 defective bottle in this sequence.
3. Calculate the Probability:
The probability of an event is calculated as the number of favorable outcomes (defective bottles) divided by the total number of outcomes (total bottles).
So, the probability [tex]\( P \)[/tex] that the next bottle is defective is:
[tex]\[
P(\text{defective}) = \frac{\text{Number of defective bottles}}{\text{Total number of bottles}} = \frac{1}{21}
\][/tex]
4. Interpreting the Result:
The calculated probability is approximately 0.0476, which means there is about a 4.76% chance that the next bottle is defective.
Therefore, the probability that the next bottle will be defective is [tex]\(\frac{1}{21}\)[/tex]. This corresponds to approximately 0.0476, which is not exactly any option provided but closest to [tex]\(\frac{1}{20}\)[/tex] when considering typical rounding in percentage terms to two decimal places.
