Probability Tools ஐ எப்படி கணக்கிடுவது
Probability Tools என்றால் என்ன?
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.
சூத்திரம்
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)
படிப்படியான வழிகாட்டி
- 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)
தீர்க்கப்பட்ட எடுத்துக்காட்டுகள்
உள்ளீடு
P(rain) = 0.4. What's P(no rain)?
முடிவு
0.6 (60%). Odds = 0.4/0.6 = 2:3
உள்ளீடு
P(A)=0.01 (disease), P(B|A)=0.95 (test given disease), P(B)=0.10
முடிவு
P(disease|positive test) = 0.095 — only 9.5%
அடிக்கடி கேட்கப்படும் கேள்விகள்
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.