如何计算Probability Tools
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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.
公式
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)
分步指南
- 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)
例题解析
输入
P(rain) = 0.4. What's P(no rain)?
结果
0.6 (60%). Odds = 0.4/0.6 = 2:3
输入
P(A)=0.01 (disease), P(B|A)=0.95 (test given disease), P(B)=0.10
结果
P(disease|positive test) = 0.095 — only 9.5%
常见问题
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.