Can someone figure out the correct answers please?

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If A and B are independent events with P(A) # 0 and P(B) # 0, then An B # 0. O True. We have that P(An B) = P(A) . P(B|A). Since P(B) # 0, then P(B|A) # 0. If An B = 0, then P(B|A) = 0. This contradiction establishes our result. O False. To establish the result that An B # 0, we need that P(A|B) # 0 and P(B|A) # 0. Thus there is not enough information given to arrive at this conclusion. O True. If An B = 0, then P(An B) = 0. Since A and B are independent events, P(An B) = P(A) . P(B) # 0, since, by our assumption, P(A) * 0 and P(B) # 0. This contradiction establishes our result. O False. If A and B are independent events, then we have that P(An B) = P(A) . P(B|A) = 0. Since P(A) # 0, then P(B|A) = 0, which occurs only when An B = 0. O False. If A and B are independent events, then by definition, An B = 0.Determine whether the statement is true or false and explain. If A is an event of an experiment, then P(A|A") 0 . (Assume P(A") # 0 .) O True. Because A U A" = U we have P(A|A") = P(AU AC) = 1. P(Ac) O P(An Ac) True. Because An Ac = U we have P(A|A) = = 1. P(Ac) O P(An Ac) False. Because An Ac = 0 we have P(A| A") = 0. P(Ac) O P(AU Ac) False. Because A U AC = 0 we have P(A| A ) = = 0. P(Ac) O P(An Ac) False. Because An Ac = U we have P(A|A") = = 0. P(Ac )Suppose that A and B are mutually exclusive events and that P(A U B) # 0. What is P(A | AUB)? O P(A) P(A) + P(B) O 2P(A) + P(B) O P(B) P(A) - P(B) O P(A) - P(B) O P(B) P(A) + P(B)