Final answer:
The probability of a game duration less than 175 minutes cannot be determined without additional information about the game's time distribution. However, the probability of waiting less than 12.5 minutes for a bus, if wait times are uniformly distributed between 0 and 15 minutes, is 83.3%. The options given seem to be incorrect as probabilities cannot exceed 100%.
Step-by-step explanation:
To analyze the probability of a game duration being fewer than 175 minutes, we need specific information regarding the distribution and parameters of the game duration times. Without these details, it's impossible to determine the probability accurately. For instance, if we knew game durations are uniformly distributed between 120 and 180 minutes, we could calculate this probability. But with no information provided in the question, we must answer "Need more information".
However, we can solve one of the provided problems regarding the uniform distribution. If we have a continuous uniform distribution for waiting times between zero and 15 minutes, the probability that a person waits fewer than 12.5 minutes is found by calculating the area under the uniform distribution curve up to 12.5 minutes.
To find this, we use the formula for the uniform distribution probability:
Probability = (x - a) / (b - a), where 'x' is the value we're looking for the probability of, and 'a' and 'b' are the minimum and maximum values of our distribution, respectively.
Here, a = 0 minutes and b = 15 minutes. Thus, Probability = (12.5 - 0) / (15 - 0) = 12.5 / 15 = 0.833 or 83.3%.
Considering this, the correct option for the probability of a person waiting fewer than 12.5 minutes for a bus would be greater than 100 percent, which is obviously a mistake in the provided options since a probability cannot exceed 100%. Therefore, there's likely a typo or some miscommunication in the question itself.