Question 1178965
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True or False: For two events A and B, suppose P(A) = 0.35, P(B) = 0.65, and P(B|A) = 0.35. Then A and B are independent.
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            From two women,  @ewatrrr and  @MathLover1,  you have two mutually exclusive answers.


            I came with my own solution  (number  3  for you)  to find out the correct answer.


            Be patient and read my post to the end.




<pre>
From given data, using the definition of the  <U>CONDITIONAL PROBABILITY</U>,  you have


    P(A &#8745; B) = P(B|A)*P(A) = 0.35*0.35 = 0.1225.


Two events, A and B, are called  <U>independent</U>  if and only if  P(A &#8745; B) = P(A)*P(B).


We just have the value  0.1225  for  P(A &#8745; B).


Now we calculate  P(A)*P(B) = 0.35*0.65 = 0.2275,  and we see that it is different from the value of  P(A &#8745; B).


HENCE,  the events A and B are  <U>N O T  I N D E P E N D E N T</U>.     <U>ANSWER</U>
</pre>

Solved.


Ignore that post which state opposite.