SOLUTION: (a)the probability that you pass the test if you understand the assignments is 80%(b) the probability of passing the test is 80% Are A & B independent events? Justify

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Question 712566: (a)the probability that you pass the test if you understand the assignments is 80%(b) the probability of passing the test is 80%
Are A & B independent events? Justify
Answer by Positive_EV(69) About Me  (Show Source):
You can put this solution on YOUR website!
A and B are independent iff P(A)*P(B) = P(A and B).
B is a sub-event of A; that is, B always happens if A happens (If you pass and understand the assignments, then you passed), but it is possible for B to happen without A as well (you pass without understanding the assignments). In other words, P(A and B) = P(A) = .8. P(A)*P(B) = .8*.8 = .64. Since P(A)*P(B) is not equal to P(A and B), the events are not independent.