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Ray Of Light [21]
2 years ago
15

The probability of event A is x, and the probaility of event B is y.

Mathematics
2 answers:
kozerog [31]2 years ago
7 0
If an event is independent, it means other events have no effect<span> on this event.

So this means P(A | B) = P(A) because A and B are independence thus event B does not change anything regarding event A.

Hope this helps.</span>
stepladder [879]2 years ago
5 0

Answer:

The condition P(A|B) = x is true.

Step-by-step explanation:

Given : The probability of event A is x, and the probability of event B is y.

If the two events are independent.

To find : Which condition must be true?  

Solution :

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

If two events are independent

Then P(A\cap B)=P(A)\times P(B)

The formulas for conditional probabilities are

P(A|B)=\dfrac{P(A\cap B)}{P(B)}\\ \\ P(B|A)=\dfrac{P(A\cap B)}{P(A)}

If we substitute the independent condition in conditional probability formulas we get,

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

Applying the given condition,

P(A/B)=P(A)=x\\\\P(B/A)=P(B)=y

Therefore, The condition P(A|B) = x is true.

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