That these events are independent?

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SUMMARY

In the discussion, Brendan inquires whether events A and B are independent given that P(A) = 0.4 and P(A|B) = 0.4. The conclusion is definitive: events A and B are independent if P(A|B) equals P(A). This is validated by the independence condition P(A ∩ B) = P(A)P(B), which confirms that the probabilities align under the independence criterion.

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brendan
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I was wondering, if you are told that for two events A and B, We Have P(A)=0.4 and $P(A\mid B) = 0.4$\\
Can you assume as P(A) = P(A\mid B) That these events are independent?
regards
Brendan
 
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Sorry guys,

That was Latex fonts

It should be
IF P(A) = 0.4 and P(A|B) = 0.4 can we assume that events A and B are independent?

regards
Brendan
 


Yes. To show this use

A, B are independent if and only if [tex]P(A\cap B)=P(A)P(B)[/tex],

[tex]P(A|B)P(B)=P(A\cap B)[/tex].
 

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