Julie is graduating from college. She has studied biology, chemistry, and comput

Question

Julie is graduating from college. She has studied biology, chemistry, and computing and hopes to work as a forensic scientist applying her science background to crime investigation. Late one night she thinks about some jobs she has applied for. Let A, B, and C be the events that Julie is offereda job by each of the following entities. A-the Connecticut Office of the Chief Medical Examiner B = the New Jersey Division of Criminal Justice C the federal Disaster Mortuary Operations Response Team Julie writes down her personal probabilities for being offered these jobs p(B) = 0.4 PLA and C) = 0.1 P(A and B and C) = 0 P(C) = 0.4 p(A) = 0.6 PLA and B) = 0.2 D(B and C) = 0.1 Make a Venn diagram of the events A, B, and C. Mark the probabilities of every intersection involving these events and their complements. A and B and C A and Bc and C AC and B and C A and B and C A and B and C A and B and C A and Bc and C AC and Bc and C

Explanation / Answer

P(A and Bc and Cc) = P(A) - P(A and B) - P(A and C) + P(A and B and C) = 0.6 - 0.2 - 0.1 + 0 = 0.3

P(Ac and Band Cc) = P(B) - P(A and B) - P(B and C) + P(A and B and C) = 0.4 - 0.2 - 0.1 + 0 = 0.1

P(Ac and Bc and C) = P(C) - P(A and C) - P(B and C) + P(A and B and C) = 0.4 - 0.1 - 0.1 + 0 = 0.2

P(A and B and Cc) = P(A and B) - P(A and B and C) = 0.2 - 0 = 0.2

P(Ac and B and C) = P(B and C) - P(A and B and C) = 0.2 - 0 = 0.2

P(A and Bc and C) = P(A and C) - P(A and B and C) = 0.1 - 0 = 0.1

P(A and B and C) = 0

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