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):
Answer by ikleyn(52900)  (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.
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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.
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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