Probability of College Students Playing Football or Baseball

Imagine a college with 300 students, divided among various extracurricular activities. In this educational institution, 62 students play football (soccer in some regions) and 23 play baseball. However, there's an interesting overlap: 14 students are talented enough to play both sports. This scenario not only reflects the diversity of student interests but also presents an interesting problem in probability.

Understanding the Basic Scenario

To calculate the probability that a randomly selected student plays either football or baseball, we need to first understand the underlying mathematics. The key here is to avoid double-counting the students who are engaged in both sports.

Let's start by summing the number of students who play each sport:

Number of students playing football: 62 Number of students playing baseball: 23

The total if we simply add these two numbers is 85. However, this figure includes the 14 students who are passionate about both sports, which are being counted twice. Therefore, we need to subtract the number of students who are counted twice:

[ 85 - 14 71 ]

Calculation of Probability

To find the probability, we use the formula for the probability of an event (P(Event)): [ P(text{Event}) frac{text{Number of favorable outcomes}}{text{Total number of possible outcomes}} ]

In our case, the number of favorable outcomes (students who play football or baseball) is 71, and the total number of possible outcomes is the total number of students, which is 300.

Therefore, the probability that a randomly selected student plays either football or baseball is:

[ P(text{Football or Baseball}) frac{71}{300} ]

Expressed as a decimal, this probability is approximately: [ 0.2367 ]

Converting this to a percentage, the probability is: [ 23.67% ]

Practical Implications

Understanding this probability is crucial for several practical purposes within the college setting. For instance, it can help in planning sports events, creating balanced teams, and determining the need for additional resources for student activities. It can also provide insights into the overall physical health and well-being of the student body.

Moreover, such statistical analysis can inform decisions about extracurricular funding and time allocation, ensuring that the activities are well-planned and effective in engaging the student population.

Conclusion

By breaking down the probability problem into its component parts, we see that the probability of a randomly selected student at this college playing football or baseball is approximately 23.67%. This understanding can be a valuable tool for both students and educators, guiding them in making informed decisions about extracurricular activities and resource allocation.

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