Question 1128416: A and B are two events.
Let P(A)=0.3 , P(B)=0.8 , and P(A and B)=0.24 .
Which statement is true?
A and B are not independent events because P(A|B)=P(A) and P(B|A)=P(B) .
A and B are not independent events because P(A|B)≠P(A) .
A and B are independent events because P(A|B)=P(A) and P(B|A)=P(B) .
A and B are not independent events because P(A|B)=P(B) and P(B|A)=P(A) .
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
P(A) = 0.3
P(B) = 0.8
P(A and B) = 0.24
P(A | B) = P(A and B)/P(B)
P(A | B) = 0.24/0.8
P(A | B) = 0.3
P(A | B) = P(A) <--- we'll use this fact
P(B | A) = P(B and A)/P(A)
P(B | A) = P(A and B)/P(A)
P(B | A) = 0.24/0.3
P(B | A) = 0.8
P(B | A) = P(B) <---- and this fact too
Since both P(A | B) = P(A) and P(B | A) = P(B) are true, this means that A and B are independent events.
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Put another way: if we know that event A occurs, then that does not change the probability P(B). So P(B | A) = P(B) meaning B is independent of A. Similarly, P(A | B) = P(A) tells us that prior knowledge of event B happening does not change the probability P(A), therefore A is independent of B.
If either P(A|B) = P(A) or P(B|A) = P(B) were false equations, then A and B would be dependent events.
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