To determine the probability of selecting a shirt that is red and medium in size from a batch of 165 shirts, we will follow these steps:
1. Identify the total number of shirts: This is the total number of possible outcomes, which is given as 165.
2. Identify the number of favorable outcomes: This is the number of shirts that are both red and medium in size, which is given as 48.
3. Calculate the probability: The probability of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes. Therefore, the probability [tex]\( P \)[/tex] of picking a red and medium shirt is calculated by dividing the number of red and medium shirts by the total number of shirts.
[tex]\[
P(\text{Red and Medium}) = \frac{\text{Number of Red and Medium shirts}}{\text{Total number of shirts}}
\][/tex]
Substituting the given numbers into the formula:
[tex]\[
P(\text{Red and Medium}) = \frac{48}{165}
\][/tex]
4. Match the calculated probability with the given options: We look for the option that matches our calculated probability.
- Option A: [tex]\(\frac{88}{165}\)[/tex]
- Option B: [tex]\(\frac{48}{165}\)[/tex]
- Option C: [tex]\(\frac{90}{165}\)[/tex]
- Option D: [tex]\(\frac{90}{27225}\)[/tex]
- Option E: [tex]\(\frac{48}{27225}\)[/tex]
The calculated probability [tex]\(\frac{48}{165}\)[/tex] matches Option B.
Therefore, the correct answer is:
B. [tex]\(\frac{48}{165}\)[/tex]
