Question 26·Medium·Probability and Conditional Probability
The membership of a school club was categorized by grade level and whether each member participates in a school sport. The results are summarized in the table below.
| Grade level | Participates in a sport | Does not participate in a sport | Total |
|---|---|---|---|
| Junior | 18 | 12 | 30 |
| Senior | 15 | 15 | 30 |
| Total | 33 | 27 | 60 |
If one of the senior members is selected at random, what fraction of these members participates in a school sport?
For table-based probability questions, first read the wording carefully to see if it is a conditional probability (for example, "if a senior is selected" or "given that the student is a junior"). Once you know the condition, restrict your attention to just that row or column of the table, then compute the probability as (desired cell) ÷ (total of that row/column). This avoids common mistakes where students accidentally use the total for the whole table instead of the total for the specified group.
Hints
Focus on the correct row
The problem says the member chosen is a senior. Which row in the table shows information just about seniors?
Decide what numbers you need
In that senior row, find how many seniors participate in a sport and how many seniors there are in total.
Set up the fraction
Probability here is a fraction: (number in the desired category) over (total in the group you are choosing from). Which number should go on top, and which on the bottom, if you are choosing from seniors only?
Desmos Guide
Compute the fraction with Desmos
From the table, determine (1) the number of seniors who participate in a sport and (2) the total number of seniors. In Desmos, type the fraction (number of senior sport participants)/(total number of seniors) and press Enter. Use the resulting fraction or decimal to match the correct answer choice.
Step-by-step Explanation
Identify the relevant group
The question says: "If one of the senior members is selected at random". That means we are only looking at seniors, not all club members.
So you should focus on the Senior row of the table.
Pick out the needed numbers from the table
From the Senior row:
- Seniors who participate in a sport:
- Seniors who do not participate in a sport:
- Total seniors:
We will use the number who participate and the total number of seniors.
Form the correct probability fraction
The fraction asked for is:
(number of seniors who participate in a sport) divided by (total number of seniors).
Using the numbers from the senior row, this fraction is
So the correct answer choice is .