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Answered

The probability of event A is x, and the probability of event B is y. If the two events are independent, which of these conditions must be true?

AP(B|A) = y
BP(A|B) = y
CP(B|A) = x
DP(A and B) = x + y

P(A and B) = x


P(A) y

Verified Answer :

The answer is A.  P(B|A)=y

Answer:

The correct options are:

      A.  P(B|A) = y

Step-by-step explanation:

We know that when two events A and B are independent.

Then,

P(A∩B)=P(A)×P(B)

As we are given:

P(A)=x and P(B)=y

Hence,

P(A∩B)=xy

Also,

\(P(A|B)=\dfrac{P(A\bigcap B)}{P(B)}\\\\\\P(A|B)=\dfrac{P(A)\times P(B)}{P(B)}\\\\\\P(A|B)=P(A)\)

Hence, P(A|B)=x

and similarly,

\(P(B|A)=\dfrac{P(A\bigcap B)}{P(A)}\\\\\\P(B|A)=\dfrac{P(A)\times P(B)}{P(A)}\\\\\\P(B|A)=P(B)\)

Hence,

  P(B|A)=y

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