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

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