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Activity1soln

# Activity1soln - Activity 1 Solutions 1 A and B are...

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Activity 1 Solutions 1 . A and B are independent events. Which of the following must be true? (4 pts) a. A and B are mutually exclusive. b. A c and B c are independent. c. ) ( ). ( ) ( B P A P B A P = d. None of the above are true 2. A simple random sample is guaranteed to reflect exactly the population from which it is drawn. (2 pts) a. True b. False 3. Consider two events, A and B, of a sample space such that P(A) = P(B) = 0.7. a. Is it possible that the two events A and B are mutually exclusive? Why or why not?( 3 pts ) No. If A and B are mutually exclusive, P(A or B)=P(A)+P(B)=1.4>1 which is not possible. b. If the events A and B are independent , what would be the probability that at least one of the two events will occur, i.e. P(A or B)? (3 pts) P(A or B)=P(A)+P(B)-P(A B)=P(A)+P(B)-P(A)P(B) =0.7+0.7-0.7*0.7 =0.91 c. Do not assume mutually exclusive or independence . Suppose that the probability of the event B occurring, given that event A has occurred, is 0.6 . What is the probability that at least one of the two events will occur, that is P(A or B)? (4 pts) P(A B)=P(B|A)P(A)=0.7*0.6=0.42.

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Activity1soln - Activity 1 Solutions 1 A and B are...

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