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P(A)=FavourableTotalP(A) = \frac{\text{Favourable}}{\text{Total}}P(A)=TotalFavourable
P(A′)=1−P(A)P(A') = 1 - P(A)P(A′)=1−P(A)
P(A∪B)=P(A)+P(B)−P(A∩B)P(A \cup B) = P(A) + P(B) - P(A \cap B)P(A∪B)=P(A)+P(B)−P(A∩B)
P(A∩B)=P(A)×P(B)P(A \cap B) = P(A) \times P(B)P(A∩B)=P(A)×P(B)
P(A∩B)=P(A)×P(B∣A)P(A \cap B) = P(A) \times P(B \mid A)P(A∩B)=P(A)×P(B∣A)
P(A∣B)=P(A∩B)P(B)P(A \mid B) = \frac{P(A \cap B)}{P(B)}P(A∣B)=P(B)P(A∩B)
Probability of BBB given AAA has occurred
P(A)=∑P(Bi)×P(A∣Bi)P(A) = \sum P(B_i) \times P(A \mid B_i)P(A)=∑P(Bi)×P(A∣Bi)
P(Bi∣A)=P(Bi)×P(A∣Bi)P(A)P(B_i \mid A) = \frac{P(B_i) \times P(A \mid B_i)}{P(A)}P(Bi∣A)=P(A)P(Bi)×P(A∣Bi)
P(At least one)=1−P(None)P(\text{At least one}) = 1 - P(\text{None})P(At least one)=1−P(None)
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