To determine the probability that a randomly selected clothing item is sweatpants, given that the size of the item is small, you need to use the concept of conditional probability.
Given:
- The total number of small-sized clothing items is 27.
- The number of small-sized sweatpants is 10.
The probability can be calculated using the formula for conditional probability:
[tex]\[ P(\text{Sweatpants} \mid \text{Small}) = \frac{\text{Number of small-sized sweatpants}}{\text{Total number of small-sized items}} \][/tex]
Plugging in the given values:
[tex]\[ P(\text{Sweatpants} \mid \text{Small}) = \frac{10}{27} \][/tex]
To express this as a percentage, you multiply the resulting fraction by 100:
[tex]\[ P(\text{Sweatpants} \mid \text{Small}) \times 100 = \left(\frac{10}{27}\right) \times 100 \approx 37.03703703703704\% \][/tex]
Therefore, the probability that a randomly selected clothing item is sweatpants, given that it is small, is approximately [tex]\( 37.04\% \)[/tex].
