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).

Question

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).

amistre64 · Answer

what is your definition of independence?

anonymous · Answer

One event doesn't depend on the other?

amistre64 · Answer

thats a little vague, how does it differ from mutually exclusive events?

anonymous · Answer

Mutually exclusive events cannot happen at the same time, but independent events can happen at the same time

anonymous · Answer

It's just that the probability of one event happening in no way affects the other happening

amistre64 · Answer

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.

amistre64 · Answer

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.

anonymous · Answer

okay, that makes sense, thank you

amistre64 · Answer

good luck :)