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Probability measures the likelihood of an event, ranging from 0 (impossible) to 1 (certain). Combined probability tools calculate unions, intersections, and conditional probabilities for multiple events.
Τύπος
P(A) = Favorable outcomes / Total outcomes | P(A and B) = P(A) × P(B) | P(A or B) = P(A) + P(B) − P(A and B)
- P(A)
- Probability of Event A (0 to 1)
- n
- Number of Outcomes (count)
Οδηγός βήμα προς βήμα
- 1Complement: P(A') = 1 − P(A)
- 2Independent events: P(A∩B) = P(A) × P(B)
- 3Union: P(A∪B) = P(A) + P(B) − P(A∩B)
- 4Bayes' theorem: P(A|B) = P(B|A) × P(A) ÷ P(B)
Worked Examples
Εισαγωγή
P(rain) = 0.4. What's P(no rain)?
Αποτέλεσμα
0.6 (60%). Odds = 0.4/0.6 = 2:3
Εισαγωγή
P(A)=0.01 (disease), P(B|A)=0.95 (test given disease), P(B)=0.10
Αποτέλεσμα
P(disease|positive test) = 0.095 — only 9.5%
Frequently Asked Questions
What does "independent events" mean?
Events are independent if the outcome of one doesn't affect the other. Rolling a die twice produces independent events.
What is conditional probability?
Conditional probability P(A|B) is the probability of A given that B has already occurred. It accounts for how new information changes odds.
What's the difference between theoretical and experimental probability?
Theoretical probability is calculated mathematically. Experimental probability comes from actual trials. With enough trials, they converge.