contestada

Which statement about events A and B is TRUE? A. If P(A | B) = P(B) and P(B | A) = P(A), then the events are dependent. B. If P(A | B) = P(B) and P(B | A) = P(A), then the events are independent. C. If P(A | B) = P(A) and P(B | A) = P(B), then the events are independent. D. If P(A | B) = P(A) and P(B | A) = P(B), then the events are dependent.

Respuesta :

Using conditional probability, it is found that the correct statement is given by:

C. If P(A | B) = P(A) and P(B | A) = P(B), then the events are independent.

What is Conditional Probability?

Conditional probability is the probability of one event happening, considering a previous event. The formula 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.

If two events are independent, we have that:

[tex]P(A \cap B) = P(A)P(B)[/tex].

Hence:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{P(A)P(B)}{P(A)} = P(B)[/tex]

[tex]P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{P(A)P(B)}{P(B)} = P(A)[/tex]

Which means that option C is correct.

More can be learned about conditional probability at https://brainly.com/question/14398287

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