Answer:
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
