To solve this problem, we need to determine the probability of picking a shirt that is both red and medium-sized from a batch of 165 shirts.
Let's start by identifying the relevant data from the table provided:
- Total number of red shirts: 90
- Number of red shirts that are medium-sized: 48
- Total number of shirts in the batch: 165
The probability of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes.
In this case, the favorable outcome is picking a shirt that is both red and medium-sized, which has 48 cases. The total number of possible outcomes is the total number of shirts, which is 165.
Therefore, the probability [tex]\( P \)[/tex] can be determined using the formula:
[tex]\[ P = \frac{\text{Number of red medium shirts}}{\text{Total number of shirts}} \][/tex]
Plugging in the numbers, we get:
[tex]\[ P = \frac{48}{165} \][/tex]
Hence, the correct answer is:
D. [tex]\(\frac{48}{165}\)[/tex]
This corresponds to a probability of approximately 0.2909090909090909 when evaluated numerically.
