Question 4·Easy·Probability and Conditional Probability
A survey taken by 1,000 students at a school asked whether they played school sports. The table below summarizes all 1,000 responses from the students surveyed.
| Males | Females | |
|---|---|---|
| Play a school sport | 312 | 220 |
| Do not play a school sport | ? | 216 |
How many of the males surveyed responded that they do not play a school sport?
For two‑way tables, remember that the four inner cells plus any row/column totals must add up to the overall total. When a single cell is missing, either (1) add the known cells and subtract from the grand total, or (2) compute row and column totals and use them to solve for the missing entry. Always check that your final table entries add back up to the stated total number of subjects (here, 1,000) to avoid common arithmetic or misreading errors.
Hints
Use the fact that there are 1,000 students total
All four cells in the table (play/do not play × male/female) together must add up to 1,000. Three of those four numbers are given. How can that help you find the missing one?
Start with the total who play a sport
Add the number of males who play (312) and the number of females who play (220). That gives the total number of students who play a school sport. How can you use this to find how many do not play?
Then separate males and females among non‑players
Once you know how many students do not play a school sport in total, subtract the 216 females who do not play. The remainder will be the males who do not play.
Desmos Guide
Compute the missing value directly
In a new expression line, type 1000 - 312 - 220 - 216. The value Desmos returns is the number of males who do not play a school sport (because you are subtracting the three known table cells from the total of 1,000).
Step-by-step Explanation
Translate the table into totals
The table describes all 1,000 students, split by two categories:
- Play vs. do not play a school sport
- Male vs. female
That means the four cells in the table (males/females × play/do not play) must add up to 1,000. Three of those cells are given; one (males who do not play) is missing.
Find how many students play and do not play a sport
First, find how many students play a school sport by adding the males and females who play:
So, 532 students play a school sport. Since there are 1,000 students total, the number who do not play a school sport is
So, 468 students do not play a school sport (males and females combined).
Isolate the males who do not play
Among the 468 students who do not play a school sport, 216 are females (given in the table). The rest must be males.
Subtract the females who do not play from the total who do not play:
So, the number of males surveyed who responded that they do not play a school sport is 252.