Final answer:
The question asks to find Madison's probability of cleaning her room on days starting with 'T', but the provided probabilities in the reference material seem unrelated to the specific question, and cannot be used to deduce the correct answer without additional context.
Step-by-step explanation:
The question requires us to determine Madison's probability of cleaning her room on a day starting with the letter 'T', which could be either Tuesday or Thursday. Since there are 7 days in a week, and 2 of them start with 'T', the probability based purely on days would be 2/7. However, the information provided suggests that Madison's probability of cleaning her room does not depend solely on the day of the week, but rather on a uniformly distributed time interval from 1 to 15 days. We can calculate the expected waiting time by taking the sum of 1 to 15 and dividing it by 15, which gives us the average. So, the expected wait time would be (1+15)/2 = 8 days, which corresponds with option A in the reference provided.
Now considering other probabilities from the reference, such as the probability that a randomly chosen student is male or has a bedroom painted with light colors (option A cannot be the correct probability since 10/118 is not an option), or the probability that a randomly chosen student is male given the student's bedroom is painted with dark colors (30/118 does not match any given option), these do not match the scenario nor the options given for Madison's probability. Thus, after evaluating the context, it seems that the reference information does not directly help us deduce Madison's cleaning probability.
Concluding, without sufficient context or relevant data, we cannot ascertain Madison's exact probability of cleaning her room on a 'T' day from the given options. For a precise answer, more specific information regarding Madison's cleaning habits or a clearer connection between her habits and the probabilities mentioned would be needed.