Question

select the correct answer.
the probability of event a is x, and the probability of event b is y.
if the two events are independent, which condition must be true?
○ a. p(b|a) = x
○ b. p(a|b) = x
○ c. p(b|a) = xy
○ d. p(a|b) = y

Explanation:

Step1: Recall the formula for conditional probability

The formula for conditional probability is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\).

Step2: Use the property of independent events

For independent events \(A\) and \(B\), \(P(A\cap B) = P(A)\times P(B)\). Given \(P(A)=x\) and \(P(B) = y\), then \(P(A\cap B)=xy\).

Step3: Calculate \(P(A|B)\)

Substitute \(P(A\cap B)=xy\) and \(P(B) = y\) into the conditional - probability formula: \(P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{xy}{y}=x\).

Answer:

B. \(P(A|B)=x\)