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Combined Probability
Chapter summary, hard words and model exam answers for ICSE Class 10 Hindi.
Free online summary and notes (ICSE Class 10 Hindi). Read it here, no PDF download needed.
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Mathematics · CBSE 10 · ICSE 10 · GCSE (AQA, Edexcel, OCR)
Summary
AND asks 'do both happen?' - multiply along the branch. OR asks 'does at least one happen?' - add the branches.
If A and B can both happen, P(A) and P(B) each count the overlap, so subtract P(A and B) once. If they cannot both happen (mutually exclusive), the overlap is zero.
Coin and die are independent. Drawing without replacement is NOT - the second probability changes, so use the new fraction.
Listing every winning case is slow; the opposite ('none') is usually one quick product. P(at least one) = 1 − P(none).
Hard words & meanings
| mutually exclusive | events that cannot both occur at the same time, so P(A and B) = 0 |
| independent events | events where the outcome of one does not change the probability of the other |
| addition rule | P(A or B) = P(A) + P(B) − P(A and B) |
| multiplication rule | P(A and B) = P(A) × P(B) for independent events |
| complement | the event that A does not happen; P(not A) = 1 − P(A) |
| with replacement | the item is put back before the next draw, keeping the probabilities the same |
| without replacement | the item is kept out, so later probabilities change |
| tree diagram | a branching diagram where you multiply along branches and add across paths |
Model exam answers, grammar & audio
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