A student says that if P(A) = P(A|B), then A and B must be independent events. Is the student correct? Explain. Give a real life example that can be represented by P(A) = P(A|B).

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A student says that if P(A) = P(A|B), then A and B must be independent events. Is the student correct? Explain. Give a real life example that can be represented by P(A) = P(A|B).

Mathematics
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what is your definition of independence?
One event doesn't depend on the other?
thats a little vague, how does it differ from mutually exclusive events?

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Mutually exclusive events cannot happen at the same time, but independent events can happen at the same time
It's just that the probability of one event happening in no way affects the other happening
correct so if the probability of an event happening, is the same for all cases ... then the probability of the event is independent of the circumstances spose there are 3 As that occur in a total of 5 Bs. P(A|B) read as, the probability of A given B, is 3/5 spose there are 6 As out of a universal set of 10 P(A|U), or simply P(A) , is 6/10 = 3/5 the probability of A is independent of the case it is a part of.
if P(A) = P(A|B) = P(A|C) = P(A|D) = ... = P(A|K) then the probability of A is the same, for all given cases, and its value does not depend on any one specific case.
okay, that makes sense, thank you
good luck :)

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