Final answer:
The question concerns finding the probability of picking a red medium shirt from a batch of 165 shirts, but without the specific number of red medium shirts, we cannot provide a definite answer. The plausible probabilities provided in the options suggest a calculation that divides the number of red medium shirts by the total number of shirts (165).
Step-by-step explanation:
The question asks for the probability of picking a red shirt that is size medium from a batch of 165 shirts. To find the probability, we would need the number of red medium shirts in the batch. The probability is calculated by dividing the number of red medium shirts by the total number of shirts, which is 165. The options given suggest that someone has previously computed the probabilities for the specific event of picking a red medium shirt.
Without additional information about how many red medium shirts there are, it's impossible to determine the correct answer. However, if we assume that the number of red medium shirts corresponds to one of the provided options, we can analyze the options to see which might make sense. Options 1) and 2) provide probabilities larger than 1/2, while options 3) and 4) offer probabilities that are very small and result from dividing small numbers (e.g., 90 or 48) by the square of the total number of shirts (27225 = 165 x 165), which seems unreasonable for a single selection. Therefore, the probabilities in options 3) and 4) are not likely to represent the probability of the event we are concerned with. Instead, one of the higher probabilities in options 1) or 2) is more plausible.