The phrase “selected from among” signals conditional probability: the group you pick from becomes the denominator. When two original groups each contribute to that group, find each eligible count and add them. Then put the target count over that combined total. Desmos can calculate the counts and the final fraction. Dividing by the entire school ignores the restriction.
Hints
- Hint 1
“From among” gives a condition, a restriction on who can be selected. Only students who play a sport are possible picks. Which students belong in the denominator?
- Hint 2
Find the intersection, the students who both have jobs and play a sport. Take of the students with jobs. Which other group also contributes sport participants?
- Hint 3
The remaining group has no part-time jobs. Find its size, then take the given fraction who play sports. Add those players to the players with jobs to get everyone who could be picked.
Step-by-step
Count the sport participants in each group
Step 1Choose the group being picked from
“From among the students who participate in a school sport” is a condition, a restriction on who can be selected. So the denominator includes sport participants with and without jobs; the numerator includes only sport participants with jobs: .Restrict the group first, then count the target inside it. Neither nor is the number of students being picked from.
- Step 2
Count sport participants with jobs
The applies to the students with jobs. Type in Desmos. It shows , the students who both have jobs and play a sport.
- Step 3
Count sport participants without jobs
The remaining students have no part-time job. Their count is . Type in Desmos. It shows students without jobs who play a sport. The applies to these remaining students, not to all .
- Step 4
Divide by all sport participants
The sport participants total , and of them have jobs. Type in Desmos. It shows about ; use the fraction button to see . So the probability that a selected sport participant has a part-time job is . Grid in 2/3.