Respuesta :
Answer:
The condition P(A|B) = x is true.
Step-by-step explanation:
Given : The probability of event A is x, and the probability of event B is y.
If the two events are independent.
To find : Which condition must be true?
Solution :
P(A)=x and P(B)=y
If two events are independent
Then [tex]P(A\cap B)=P(A)\times P(B)[/tex]
The formulas for conditional probabilities are
[tex]P(A|B)=\dfrac{P(A\cap B)}{P(B)}\\ \\ P(B|A)=\dfrac{P(A\cap B)}{P(A)}[/tex]
If we substitute the independent condition in conditional probability formulas we get,
[tex]P(A|B)=\dfrac{P(A\cap B)}{P(B)}=\dfrac{P(A)\times P(B)}{P(B)}=P(A)\\ \\ P(B|A)=\dfrac{P(A\cap B)}{P(A)}=\dfrac{P(A)\times P(B)}{P(A)}=P(B)[/tex]
Applying the given condition,
[tex]P(A/B)=P(A)=x\\\\P(B/A)=P(B)=y[/tex]
Therefore, The condition P(A|B) = x is true.
