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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)

2 Answers

3 votes
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.
User Alexander Doroshko
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2 votes

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,


P(A\cap B)=P(A)* P(B).

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


P(A/B)=(P(A\cap B))/(P(B))=(P(A) * P(B))/(P(B))=P(A).

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

Option (B) is CORRECT.

User Ryan Walls
by
7.9k points

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