Final answer:
The probability of choosing an orange shirt today and a red shirt tomorrow, given 'a' shirts in total, is the product of two probabilities: '1/a' for the orange shirt and '1/(a-1)' for the red shirt, after setting the orange shirt aside.
Step-by-step explanation:
The question pertains to the field of probability, a mathematical concept that deals with the likelihood of occurrence of a random event. The scenario presented involves choosing shirts of different colors on successive days. Specifically, the question seeks the probability of selecting an orange shirt today and a red shirt tomorrow. To calculate this, we must assume there is a fixed number of shirts in total, including at least one orange and one red shirt.
Assuming there are 'a' shirts in total, the probability of picking an orange shirt on the first day would be '1/a' since there is only one orange shirt. After selecting the orange shirt, there would be 'a-1' shirts left for the second day. If we assume there is only one red shirt, then the probability of selecting the red shirt on the second day is '1/(a-1)'. To find the combined probability of both events occurring consecutively, we multiply the individual probabilities together.
Therefore, the combined probability of picking the orange shirt first and then the red shirt is '1/a * 1/(a-1)'.