Question 1176346
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A and B are independent events. P(A|B) = 0.4. Find P(A).
Round your answer to the nearest tenth.
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<pre>
By the definition of the conditional probability,


    P(A|B) = {{{P(Q_and_B)/P(B)}}}.     (1)


By the definition, the events A and B are independent if 


    P(A and B) = P(A)*P(B).             (2)


By substituting (2) into (1), you have


    P(A|B) = {{{(P(A)*P(B))/P(B)}}} = P(A).


But P(A|B) is given: it is 0.4.


Therefore, at given conditions,  P(A) = 0.4.      <U>ANSWER</U>.
</pre>

Solved.


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This result justifies the name of independent events: 


<pre>
    for independent events A and B,  P(A|B)  does not depend on P(B) and is equal to P(A).
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