Answer :
To solve this problem, we need to determine the probability that a randomly selected clothing item is a pair of sweatpants given that it's of small size. Let's break down the steps involved in finding this probability:
1. Determine the Total Number of Small Size Clothing Items Sold:
According to the table, the total number of small size clothing items sold is 27.
2. Find the Number of Small Size Sweatpants Sold:
From the table, we see that 10 small size sweatpants were sold.
3. Calculate the Conditional Probability:
The conditional probability [tex]\( P(\text{Sweatpants} \mid \text{Small}) \)[/tex] is given by the ratio of the number of small sweatpants to the total number of small size clothing items. This is calculated as:
[tex]\[ P(\text{Sweatpants} \mid \text{Small}) = \frac{\text{Number of Small Sweatpants}}{\text{Total Number of Small Size Clothing Items}} = \frac{10}{27} \][/tex]
4. Convert the Probability to a Percentage:
To express this probability as a percentage, multiply the ratio by 100:
[tex]\[ \text{Probability Percentage} = \left( \frac{10}{27} \right) \times 100 \approx 37.03703703703704 \][/tex]
5. Round to the Nearest Whole Percent:
Finally, we round the percentage to the nearest whole number:
[tex]\[ 37.03703703703704 \approx 37 \][/tex]
Thus, the probability that a randomly selected clothing item is a pair of sweatpants given that it's of small size is approximately 37%.
Therefore,
[tex]\[ P(\text{Sweatpants} \mid \text{Small}) \approx 37 \% \][/tex]
1. Determine the Total Number of Small Size Clothing Items Sold:
According to the table, the total number of small size clothing items sold is 27.
2. Find the Number of Small Size Sweatpants Sold:
From the table, we see that 10 small size sweatpants were sold.
3. Calculate the Conditional Probability:
The conditional probability [tex]\( P(\text{Sweatpants} \mid \text{Small}) \)[/tex] is given by the ratio of the number of small sweatpants to the total number of small size clothing items. This is calculated as:
[tex]\[ P(\text{Sweatpants} \mid \text{Small}) = \frac{\text{Number of Small Sweatpants}}{\text{Total Number of Small Size Clothing Items}} = \frac{10}{27} \][/tex]
4. Convert the Probability to a Percentage:
To express this probability as a percentage, multiply the ratio by 100:
[tex]\[ \text{Probability Percentage} = \left( \frac{10}{27} \right) \times 100 \approx 37.03703703703704 \][/tex]
5. Round to the Nearest Whole Percent:
Finally, we round the percentage to the nearest whole number:
[tex]\[ 37.03703703703704 \approx 37 \][/tex]
Thus, the probability that a randomly selected clothing item is a pair of sweatpants given that it's of small size is approximately 37%.
Therefore,
[tex]\[ P(\text{Sweatpants} \mid \text{Small}) \approx 37 \% \][/tex]
