Respuesta :
Answer:
B.) P(A/B) = P(A)
Step-by-step explanation:
If two events, A and B are independent:
We have that:
[tex]P(A \cap B) = P(A)P(B)[/tex]
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
Since they are independent:
[tex]P(A \cap B) = P(A)P(B)[/tex]
Then
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{P(A)P(B)}{P(A)} = P(B)[/tex]
So
[tex]P(B|A) = P(B)[/tex], or either:
[tex]P(A|B) = P(A)[/tex], and thus, the correct answer is given by option B.
