Below a two-way table is given for student activities:
| | Sports | Drama | Work | Total |
| -------- | ------ | ----- | ---- | ----- |
| Sophomore | 20 | 7 | 3 | 30 |
| Junior | 20 | 13 | 2 | 35 |
| Senior | 25 | 5 | 5 | 35 |
| Total | 65 | 25 | 10 | 100 |
Follow the steps to find the probability a student is in sports, given that they are a senior.
Next, find the probability that it's a senior in sports.
[tex]P(\text { senior })=0.35[/tex] [tex]P(\text { senior and sports })=[/tex][?]
Enter your answer in decimal form. Do not round.
Answer (2)
Find the number of seniors in sports from the table: 25.
Divide the number of seniors in sports by the total number of students: 100 25 .
Calculate the probability: 0.25.
The probability that a student is a senior and participates in sports is 0.25 .
Explanation
Analyze the problem We are given a two-way table that shows the distribution of students across different activities (Sports, Drama, Work) and grade levels (Sophomore, Junior, Senior). The goal is to find the probability that a student is a senior and participates in sports.
Identify the number of seniors in sports From the table, we can see that there are 25 seniors who participate in sports. The total number of students is 100.
Calculate the probability To find the probability that a student is a senior and participates in sports, we divide the number of seniors in sports by the total number of students: P ( " se ni or an d s p or t s " ) = Total number of students Number of seniors in sports = 100 25 = 0.25
State the final answer Therefore, the probability that a student is a senior and participates in sports is 0.25.
Examples
This type of probability calculation is useful in various real-life scenarios, such as analyzing survey data to understand the relationship between different categories. For example, a school might want to know the probability that a student is both a senior and involved in sports to better allocate resources or plan activities. The probability of a student being a senior and in sports is calculated by dividing the number of seniors in sports by the total number of students. In this case, with 25 seniors in sports out of 100 total students, the probability is 100 25 = 0.25 .
The probability that a student is a senior and participates in sports is 0.25. This means that there is a 25% chance that a randomly selected student is both a senior and involved in sports activities. Therefore, P(senior and sports) is calculated as 100 25 .
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