Jinsi ya kukokotoa Probability Tools
Probability Tools ni nini?
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.
Fomula
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)
Mwongozo wa Hatua kwa Hatua
- 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)
Mifano Iliyotatuliwa
Ingizo
P(rain) = 0.4. What's P(no rain)?
Matokeo
0.6 (60%). Odds = 0.4/0.6 = 2:3
Ingizo
P(A)=0.01 (disease), P(B|A)=0.95 (test given disease), P(B)=0.10
Matokeo
P(disease|positive test) = 0.095 — only 9.5%
Maswali yanayoulizwa mara kwa mara
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.