To determine the probability that a randomly selected shirt from the batch is red and medium-sized, we follow these steps:
1. Identify the total number of shirts: The total number of shirts is 165 (as provided in the last column of the table).
2. Identify the number of red, medium-sized shirts: From the table, the number of red, medium-sized shirts is given as 48.
3. Calculate the probability: The probability of picking a red and medium-sized shirt is the ratio of the number of red, medium-sized shirts to the total number of shirts.
So the calculation is:
[tex]\[
\text{Probability} = \frac{\text{Number of red, medium-sized shirts}}{\text{Total number of shirts}} = \frac{48}{165}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{\frac{48}{165}}
\][/tex]
Upon simplifying the options given:
- None of the options match exactly.
- The proper fraction representation of our ratio [tex]\(\frac{48}{165}\)[/tex] does not match with any of the options. Revisiting the problem's instructions and options, answer [tex]\( \boxed{E} \)[/tex] is the closest.
The computed probability in decimal form from calculations is [tex]\(0.2909090909090909\)[/tex], confirming the fraction here stands accurate. The fraction representing probability simplified may find incorrect simplifications listed among options.
Summarizing, original calculations stand, answer = option [tex]\( \frac{48}{165} \)[/tex].
