Answer :
To address the question of determining the probability that a randomly selected clothing item is a T-shirt given that it is large, we need to follow these steps:
1. Identify the total number of large clothing items sold.
From the table, we see:
- Total large clothing items = [tex]\(33\)[/tex]
2. Identify the number of large T-shirts sold.
From the table, we see:
- Number of large T-shirts sold = [tex]\(8\)[/tex]
3. Calculate the conditional probability [tex]\( P(\text{T-Shirt | Large}) \)[/tex]:
The probability of an event given conditioning on another event is calculated by dividing the number of favorable outcomes by the total number of outcomes under the given condition.
[tex]\[ P(\text{T-Shirt | Large}) = \frac{\text{Number of large T-shirts}}{\text{Total number of large items}} \][/tex]
Substituting the values we have:
[tex]\[ P(\text{T-Shirt | Large}) = \frac{8}{33} \][/tex]
4. Convert this probability into a percentage:
To express this probability as a percentage, we multiply by 100:
[tex]\[ P(\text{T-Shirt | Large}) = \left( \frac{8}{33} \right) \times 100 \][/tex]
The result of this calculation is approximately [tex]\(24.242424242424242\%\)[/tex].
5. Round the percentage to the nearest whole number:
Hence, [tex]\(24.242424242424242\%\)[/tex] rounds to [tex]\(24\%\)[/tex].
Therefore, the probability that a randomly selected clothing item from this store is a T-shirt, given that it is large, is:
[tex]\[ P(\text{T-Shirt | Large}) \approx 24\% \][/tex]
Thus, the final answer is:
[tex]\[ 24\% \][/tex]
1. Identify the total number of large clothing items sold.
From the table, we see:
- Total large clothing items = [tex]\(33\)[/tex]
2. Identify the number of large T-shirts sold.
From the table, we see:
- Number of large T-shirts sold = [tex]\(8\)[/tex]
3. Calculate the conditional probability [tex]\( P(\text{T-Shirt | Large}) \)[/tex]:
The probability of an event given conditioning on another event is calculated by dividing the number of favorable outcomes by the total number of outcomes under the given condition.
[tex]\[ P(\text{T-Shirt | Large}) = \frac{\text{Number of large T-shirts}}{\text{Total number of large items}} \][/tex]
Substituting the values we have:
[tex]\[ P(\text{T-Shirt | Large}) = \frac{8}{33} \][/tex]
4. Convert this probability into a percentage:
To express this probability as a percentage, we multiply by 100:
[tex]\[ P(\text{T-Shirt | Large}) = \left( \frac{8}{33} \right) \times 100 \][/tex]
The result of this calculation is approximately [tex]\(24.242424242424242\%\)[/tex].
5. Round the percentage to the nearest whole number:
Hence, [tex]\(24.242424242424242\%\)[/tex] rounds to [tex]\(24\%\)[/tex].
Therefore, the probability that a randomly selected clothing item from this store is a T-shirt, given that it is large, is:
[tex]\[ P(\text{T-Shirt | Large}) \approx 24\% \][/tex]
Thus, the final answer is:
[tex]\[ 24\% \][/tex]
