Independent events
The question
| Chess | Cards | Total | |
|---|---|---|---|
| Juniors | 6 | 24 | 30 |
| Seniors | 64 | 6 | 70 |
| Total | 70 | 30 | 100 |
Are Juniors and Chess independent?
IndependentNot independent
Are the two events independent?
How it works.
P = 30%·P = 70%
30% × 70%=21%
table 6%≠predicted 21%→Not independent
- 01
30 of the 100 are Juniors and 70 are Chess, so P(Juniors) is 30% and P(Chess) is 70%.
- 02
If the two had nothing to do with each other, the share who are BOTH would be one share OF the other: 30% × 70% = 21%.
- 03
The table shows 6 of the 100 in that corner, not 21 — 15 percentage points fewer than independence predicts. Knowing one DOES change the other, so they are not independent.