Probability Of Selecting A Male Student From Movie Attendees A Mathematical Analysis
In this article, we will analyze the probability of randomly selecting a male student from a group of students who attended two different movies: Action and Romance. This is a fundamental problem in probability theory, often encountered in introductory statistics and mathematics courses. We will walk through the steps to calculate this probability, ensuring a clear and comprehensive understanding of the process. Understanding probability is essential in various fields, including data analysis, decision-making, and risk assessment. This article aims to provide not just the solution, but also a detailed explanation that enhances your grasp of probability concepts.
Understanding the Data
Before we dive into the calculations, let's discuss the importance of understanding the data presented in the table. The table provides a structured overview of the number of male and female students who attended either the Action movie or the Romance movie. Each cell in the table represents a specific subgroup, such as the number of male students who watched the Action movie. The totals for each row and column are also crucial as they provide the marginal distributions, which are essential for calculating probabilities.
To begin, let's consider a scenario where we have a table showing the number of male and female students who attended two different movies, Action and Romance. The data is presented in the following format:
| Action | Romance | |
|---|---|---|
| Male | 30 | 45 |
| Female | 25 | 50 |
This table is the foundation for our probability calculation. It provides a clear overview of the distribution of students across different categories. For instance, we can see that 30 male students watched the Action movie, while 45 male students watched the Romance movie. Similarly, 25 female students attended the Action movie, and 50 female students watched the Romance movie. The structure of the table allows us to easily extract and utilize the necessary information for our calculations.
Key Data Points
- Male students who watched Action: 30
- Male students who watched Romance: 45
- Female students who watched Action: 25
- Female students who watched Romance: 50
These figures are crucial for determining the total number of male students, the total number of students, and ultimately, the probability of selecting a male student at random.
Calculating the Total Number of Students
To calculate the probability, we first need to determine the total number of students in the group. This involves summing up the number of students in each category (Male/Action, Male/Romance, Female/Action, Female/Romance). Accurately calculating the total number of students is a critical step in determining the probability. If this number is incorrect, the subsequent probability calculation will also be flawed. Therefore, it is essential to double-check the summation to ensure accuracy.
Step-by-Step Calculation
- Add the number of male students who watched the Action movie (30) and the Romance movie (45): 30 + 45 = 75
- Add the number of female students who watched the Action movie (25) and the Romance movie (50): 25 + 50 = 75
- Add the total number of male students (75) and the total number of female students (75): 75 + 75 = 150
Therefore, the total number of students in the group is 150. This number serves as the denominator in our probability calculation. It represents the entire sample space from which we are selecting a student at random.
Determining the Total Number of Male Students
Next, we need to find the total number of male students. This can be done by adding the number of male students who watched the Action movie and the number of male students who watched the Romance movie. Identifying the total number of male students is a key component in calculating the probability of selecting a male student. This number will serve as the numerator in our probability fraction.
Calculation
To find the total number of male students, we add the number of male students who watched the Action movie (30) to the number of male students who watched the Romance movie (45):
30 + 45 = 75
Thus, there are 75 male students in the group. This figure is crucial for the next step, where we calculate the probability.
Calculating the Probability
Now that we have the total number of students (150) and the total number of male students (75), we can calculate the probability of randomly selecting a male student. Probability is defined as the number of favorable outcomes divided by the total number of possible outcomes. In this case, the favorable outcome is selecting a male student, and the total possible outcomes are all the students in the group.
Probability Formula
The formula for probability is:
Probability (Male) = (Total Number of Male Students) / (Total Number of Students)
Applying the Formula
Using the values we calculated:
Probability (Male) = 75 / 150
Simplifying the Fraction
We can simplify the fraction 75/150 by dividing both the numerator and the denominator by their greatest common divisor, which is 75:
75 / 150 = (75 ÷ 75) / (150 ÷ 75) = 1 / 2
So, the probability of selecting a male student is 1/2, or 0.5 in decimal form.
Rounding the Answer
The question asks us to round the answer to two decimal places. Since 0.5 already has one decimal place, we can simply add a zero to the end to meet the requirement.
Rounded Probability
- 5 rounded to two decimal places is 0.50.
Therefore, the probability that a randomly chosen person from this group is male, rounded to two decimal places, is 0.50.
In conclusion, by following a step-by-step approach, we have successfully calculated the probability of selecting a male student from the given group. We began by understanding the data presented in the table, then calculated the total number of students and the total number of male students. Using these values, we applied the probability formula to find the probability and rounded the answer to the specified decimal places.
The probability that a randomly chosen person from this group is male is 0.50. This detailed explanation not only provides the answer but also reinforces the principles of probability calculation, ensuring a solid understanding of the topic.
