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. $p(b|a) = xy$
b. $p(a|b) = x$
c. $p(b|a) = x$
d. $p(a|b) = y$

Explanation:

Step1: Recall independent events rule

For independent events \(A\) and \(B\), \(P(A|B) = P(A)\) and \(P(B|A) = P(B)\). We know \(P(A)=x\), \(P(B)=y\).

Step2: Match to options

Check each option against the rule:

• A: \(P(B|A)=xy\) is false, since \(P(B|A)=y\)
• B: \(P(A|B)=x\) matches \(P(A|B)=P(A)=x\)
• C: \(P(B|A)=x\) is false, since \(P(B|A)=y\)
• D: \(P(A|B)=y\) is false, since \(P(A|B)=x\)

Answer:

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