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3. Two events
Give P(A), P(B), and P(A and B). Venn questions, given, independent, mutually exclusive.
| Case | B | not B | Total |
|---|---|---|---|
| A | 0.3 | 0.3 | 0.6 |
| not A | 0.2 | 0.2 | 0.4 |
| Total | 0.5 | 0.5 | 1 |
- P(A or B)0.80.6 + 0.5 − 0.3. Subtract the overlap once.
- P(A | B)0.60.3 ÷ 0.5. B is the new total.
- P(B | A)0.50.3 ÷ 0.6
- P(not A)0.41 − 0.6
- P(neither)0.21 − P(A or B)
- P(A only)0.30.6 − 0.3
- P(exactly one)0.5P(A or B) − P(A and B)
- Independent?YesP(A) × P(B) = 0.3 equals P(A and B) = 0.3.
- Mutually exclusive?NoThey overlap, P(A and B) = 0.3.