Final answer:
The probability that a senior student is going to college and plays sports is 25%, while the probability of a senior taking a gap year is 10%. Additional probabilities would require further details but are calculated using basic rules of probability.
Step-by-step explanation:
The question pertains to calculating the probability that a senior student is either going to college and plays sports, or is taking a gap year. Based on the information, it is given that there are 200 seniors, with 140 going to college, 40 directly to work, and the remainder taking a gap year. To find the probability that a senior is going to college and plays on a sports team, we consider that there are 50 seniors who fulfil this condition. Thus, the probability is 50 out of 200 or 25%. Similarly, the remainder who are not going to college or work are taking a gap year; this is 200 - 140 - 40 = 20 students. The probability of a senior taking a gap year is therefore 20 out of 200 or 10%.
For the additional questions without enough information, we would typically use the total number of seniors, the specific quantity within a category, and basic probability rules to calculate the required probabilities. For example, for estimating how many seniors participated in after-school sports all four years, we would base our calculations on the given percentage and the total number of students.