Darasa la 9–12Probability & StatisticsImepangwa
Conditional probability and independence
Addition and multiplication rules, conditional probability, independence, Bayes' theorem in simple cases, and probabilities computed by counting.
math.prob.probability-rules
Somo la mada hii bado halijaandikwa. Muhtasari ulio hapa chini ni sehemu ya ramani ya mtaala na haujakaguliwa.
Inajengwa juu ya
Masharti ya awali ya lazima 18 (hadi chini kabisa)
Utajifunza
- Compute conditional probabilities from two-way tables and tree diagrams.
- Decide whether events are independent, and distinguish independence from mutual exclusivity.
- Apply Bayes' theorem to problems such as diagnostic testing with base rates.
Fasili
- For P(B) > 0, the conditional probability of A given B is P(A | B) = P(A ∩ B)/P(B).
- Events A and B are independent if P(A ∩ B) = P(A)P(B).
- Events A and B are mutually exclusive if they cannot both occur, that is, A ∩ B = ∅.
Nadharia
- P(A ∪ B) = P(A) + P(B) − P(A ∩ B).
- Bayes' theorem: P(A | B) = P(B | A)P(A)/P(B) when P(B) > 0.
- Law of total probability: if B₁, …, Bₙ partition the sample space, P(A) = Σ P(A | Bᵢ)P(Bᵢ).
- Two mutually exclusive events with positive probabilities are never independent.
Mawazo potofu ya kawaida
- Confusing P(A | B) with P(B | A) (the prosecutor's fallacy).
- Ignoring base rates when interpreting a positive test result.
- Thinking 'independent' means 'mutually exclusive'.
Inaelekea kwa
Ugunduzi wa hiari
- Statistical inference Bayesian statistics uses Bayes' theorem to update beliefs about unknown quantities in the light of data.