Etottemstula
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A and B are independent events. Which equation below must be true?
A. P(A) = P(B)
B. P(A | B) = P(A)
C. P(A ∩ B) = P(A)
D. P(B) = P(A | B)

Respuesta :

Hagrid
A and B are independent events. The equation below that must be true is P(A | B) = P(A). The answer is letter B. The rest of the choices do not answer the question above.

Answer:  The correct option is (B)  P(A | B) = P(A)

Step-by-step explanation:  Given that A and B are independent events.

We are to select the TRUE  statement from the given options.

We know that

if two events A and B are independent events, then the probability of the intersection of A and B is equal to the product of the probabilities of the events A and B.

That is,

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

Now, the conditional probability of event A given that event B has already occured is given by

[tex]P(A/B)=\dfrac{P(A\cap B)}{P(B)}=\dfrac{P(A) \times P(B)}{P(B)}=P(A).[/tex]

Thus, the correct statement is  P(A | B) = P(A).

Option (B) is CORRECT.

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