Let's determine the probability that a randomly selected clothing item is medium, given that it is a sweatshirt. The given data from the table is as follows:
- Total number of sweatshirts: 35
- Number of sweatshirts that are medium: 11
We need to find the conditional probability [tex]\( P(\text{Medium} \mid \text{Sweatshirt}) \)[/tex], which is the probability that an item is medium-sized given that it is a sweatshirt. The formula for conditional probability is:
[tex]\[ P(\text{Medium} \mid \text{Sweatshirt}) = \frac{\text{Number of Medium Sweatshirts}}{\text{Total Number of Sweatshirts}} \][/tex]
Substitute the values:
[tex]\[ P(\text{Medium} \mid \text{Sweatshirt}) = \frac{11}{35} \][/tex]
Next, we convert this probability to a percentage by multiplying by 100:
[tex]\[ P(\text{Medium} \mid \text{Sweatshirt}) \times 100 = \left( \frac{11}{35} \right) \times 100 \approx 31.42857142857143 \][/tex]
Rounding to the nearest whole number:
[tex]\[ \approx 31\% \][/tex]
Therefore, the probability that a randomly selected clothing item is medium, given that it is a sweatshirt, is:
[tex]\[ P(\text{Medium} \mid \text{Sweatshirt}) = 31\% \][/tex]
