Final answer:
The probability that a student plays both football and basketball requires specific participation data to calculate. The procedure typically involves calculating marginal distributions from a provided data set, or using the binomial probability formula if given a success rate and a sample size for an entire population.
Step-by-step explanation:
The question relates to the probability that a student plays both football and basketball. To determine this probability, we need specific data on the number of students playing both sports. Without such data, we can only speak in general terms or use given data about related situations. For example, if we have a two-way table showing the types of college sports played by gender, it can provide the raw data needed to calculate marginal distributions and joint probabilities, which can be then used to find the probability of a student playing both football and basketball.
When trying to determine the probability that a senior is going to college and plays sports, we consider the number of seniors going to college and are on their school's sports teams. If there are 50 seniors going to college who are on sports teams, and this is out of a known total number of college-bound seniors, we can calculate the probability by dividing 50 by the total number of college-bound seniors.
To find the likelihood of a certain number of students participating in after-school sports all four years based on a percentage, we use the binomial probability formula. For example, given that 8 percent of students participate all four years and we have a sample of 60 students, we can calculate the probability of exactly four or five students participating using the binomial probability formula which incorporates the success probability (p = 0.08), the number of trials (n = 60), and the desired number of successes (k = 4 or 5).