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 offered a job by 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(A) = 0.6 PA and B) = 0.1 p(B and C) = 0.1 p(B) = 0.4 P(A and C) 0.2 p(A and B and C)- P(C) = 0.4 Make a venn diagram of the events A, B, and C. Markthe probabilities of every intersection involving these events and their complements. Use this diagram to answer the following A and B and C A and Be and c A and B and C Ac and B and C A and B and C Ac and B and C

Explanation / Answer

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

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

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

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

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

P(A and B and C) = 0

P(A or B or C) = P(A) + P(B) + P(C) - P(A and B) - P(A and C) - P(B and C) + P(A and B and C)

= 0.6 + 0.4 + 0.4 - 0.1 - 0.2 - 0.1

= 1

P(Ac and Bc and Cc) = 1 - P(A or B or C) = 1 - 1 = 0

b) P(B | C) = P(B and C) / P(C) = 0.1 / 0.4 = 0.25

c) P(C | B) = P(B and C) / P(B) = 0.1 / 0.4 = 0.25

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