Finish formulas for properties of probabilities: 4) P(A ∪ B) = P(A) + P(B) - P(A ∩ B) (dependent events). P(A ∩ B) = P(A) * P(B) (independent events). P(A ∪ B) = P(A) + P(B) (incompatible events).
Added by Jose Angel S.
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It states that the probability of the union of two events A and Z is equal to the sum of their individual probabilities minus the probability of their intersection. 4b) P(Aob) = P(A) + P(B) - P(A∩B) Show more…
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The probability of sum of the incompatible events A and B can be compute by such formula P(AB) = P(A) * P(B/A) P(AB) = P(A) * P(B) P(A + B) = P(A) + P(B) P(A + B) = P(A) + P(B) - P(AB)
Adi S.
For each set of probabilities, determine whether the events A and B are independent or dependent: Probabilities Independent Dependent (a) P(A) = 1/2; P(B) = 1/6; P(A|B) = 1/2 (b) P(A) = 1/6; P(B) = 1/4; P(A|B) = 1/5 (c) P(A) = 1/2; P(B) = 1/4; P(A and B) = 1/8 (d) P(A) = 1/3; P(B) = 1/6; P(B|A) = 1/2
Manisha S.
4. (10 Points) Recall the formula we discussed in class P(A ∪ B) = P(A) + P(B) - P(A ∩ B) Using this formula, prove that for any three events A, B, C we have the following identity P(A ∪ B ∪ C) = P(A) + P(B) + P(C) - P(A ∩ B) - P(B ∩ C) - P(A ∩ C) + P(A ∩ B ∩ C) You may also recall the distributive formula for probability of events/sets.
Sri K.
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