Final answer:
The questions cannot be accurately answered without further context regarding probability distribution or event outcomes. Probability theory, including the sum rule and product rule, is usually applied to determine expected values and probabilities.
Step-by-step explanation:
The probability of the difference of scores being a specific number is not fully clear based on the information provided; it would normally be calculated based on a given context, such as dice rolls, card draws, or another probabilistic event. To find the probabilities and the most likely values, we often utilize probability theory principles such as the sum rule and product rule.
In the context of probability, an expected value is a weighted average of all possible outcomes, where each outcome is weighted by its probability of occurring. To calculate the expected value, you multiply each outcome by its probability and sum these products.
Without full context or additional data given, it is not possible to accurately determine which of the options (a), (b), (c), or (d) is correct. To answer the question correctly, specific values such as the probability distribution of having a certain number of children or the probabilities associated with throwing dice would be required.