Probability Tools کا حساب کیسے لگائیں
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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.
فارمولا
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)
مرحلہ وار گائیڈ
- 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)
حل شدہ مثالیں
ان پٹ
P(rain) = 0.4. What's P(no rain)?
نتیجہ
0.6 (60%). Odds = 0.4/0.6 = 2:3
ان پٹ
P(A)=0.01 (disease), P(B|A)=0.95 (test given disease), P(B)=0.10
نتیجہ
P(disease|positive test) = 0.095 — only 9.5%
اکثر پوچھے جانے والے سوالات
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.