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17 July, 08:25

A and b are independent events p (a) =.50 P (b) =.20 what is p (A/B)

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  1. 17 July, 08:39
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    P (a|b) = 1/2

    Step-by-step explanation:

    * Lets study the meaning independent probability

    - Two events are independent if the result of the second event is not

    affected by the result of the first event

    - If A and B are independent events, the probability of both events

    is the product of the probabilities of the both events

    - P (A and B) = P (A) · P (B) ⇒ P (A ∩ B) = P (A) · P (B)

    - If A and B are two events, then the conditional probability of A

    given B is defined as P (A|B) = P (A∩B) / P (B)

    * Lets solve the problem

    ∵ P (a) = 0.50

    ∵ P (b) = 0.20

    ∵ a and b are independent events

    ∴ P (a ∩ b) = P (a) · P (b)

    ∴ P (a ∩ b) = 0.50 * 0.20 = 0.10

    ∵ P (a|b) = P (a∩b) / P (b)

    ∴ P (a|b) = 0.10/0.20 = 1/2

    * P (a|b) = 1/2
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