SOLUTION: 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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Question 1178965: 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.
Found 3 solutions by ewatrrr, MathLover1, ikleyn:
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!

P(Independent Events) = the product of the individual probabilities.
P(A|B) = P(A and B)/P(B) = (.35)(.65)/(.65)= .35
Yes, A and B are independent.
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!


given


(|) =

Two events A and B are independent if and only if :
(|)=
(|)=
( ∩ )=
as you can see from given:
(|)≠, events and are independent






Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
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.
~~~~~~~~~~~~~~~


            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. 



From given data, using the definition of the  CONDITIONAL PROBABILITY,  you have


    P(A ∩ B) = P(B|A)*P(A) = 0.35*0.35 = 0.1225.


Two events, A and B, are called  independent  if and only if  P(A ∩ B) = P(A)*P(B).


We just have the value  0.1225  for  P(A ∩ 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 ∩ B).


HENCE,  the events A and B are  N O T  I N D E P E N D E N T.     ANSWER

Solved.

Ignore that post which state opposite.



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