03 / 12 · Count the chances
Which group are you counting in?
Find the right total when the question gives you a condition.
Builds on Does the first draw change the second?
Go to practice ↓A question to keep in mind
Among morning students, how many prefer tea? Is that the same question as the reverse?
'Among morning students' means put everyone else aside. The total is now the 8 morning students, not all 20 students.
A probability within a specified group is a conditional probability. Reversing the question usually changes the group you divide by, even if the people in the overlap are the same.
Work through an example
| Class | Tea | Coffee | Total |
|---|---|---|---|
| Morning | 6 | 2 | 8 |
| Afternoon | 3 | 9 | 12 |
| Total | 9 | 11 | 20 |
- Among morning students: use the morning row, total 8.
- Six prefer tea, so 6 / 8 = 75%.
- Among tea drinkers instead: total 9, of whom 6 are morning students. Now it is 6/9, not 6/8.
Your turn
0 / 3Among morning students, what are the total, the tea count, and the tea percentage?
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- Morning students: 8
- Morning students who prefer tea: 6
- Tea among morning students: 75 %
The group contains 8 students, 6 of whom prefer tea. 6/8 is 75%.
Among students who prefer tea, what fraction attends the morning class?
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6/9
The six people in the overlap did not change. The denominator changed from 8 to 9 because the question changed.
Pick uniformly from the afternoon students. What is the chance they prefer coffee?
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9/12 = 75%
The same rule works in a new row: first find the group, then count the wanted outcome within it.
Bring it back to your own work
Write two questions with the same overlap but different groups, such as 'artists among students' and 'students among artists'. State each denominator.
Statistical literacy: directory, audit and transfer assessment
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