Statistics / Unit 6: Probability
6.5 Two-Way Tables
Notes
A two-way table shows counts for two categorical variables. From it you can find joint, marginal and conditional probabilities.
- Joint: both things happen (a cell divided by the grand total). Marginal: one variable alone (a row or column total divided by the grand total).
- Conditional: restrict to one row or column and divide by that total.
- Example: A class of 100 has 50 boys and 50 girls. 30 boys and 24 girls play a sport, so 54 play a sport.
| Sport | No sport | Total | |
|---|---|---|---|
| Boys | 30 | 20 | 50 |
| Girls | 24 | 26 | 50 |
| Total | 54 | 46 | 100 |
- $\displaystyle P(\text{sport}) = \frac{54}{100}$ and $\displaystyle P(\text{sport} \mid \text{girl}) = \frac{24}{50}$.
Practice
In a class of 100 students, 50 are boys and 50 are girls. 30 boys and 24 girls play a sport. What is the probability a randomly chosen student plays a sport?
$\displaystyle \frac{30 + 24}{100} = 0.54$.
For a class (50 boys, 50 girls, 30 boys and 24 girls play a sport), what is $P(\text{plays a sport} \mid \text{girl})$?
Restrict to the 50 girls, of whom 24 play a sport.
A class has 50 boys and 50 girls; 30 boys and 24 girls play a sport. What is $P(\text{girl} \mid \text{plays a sport})$? (Round to 2 decimals.)
Restrict to the 54 athletes, of whom 24 are girls: $\displaystyle \frac{24}{54} \approx 0.44$.
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