3. Consider a Venn diagram, where P(E) = .10, P(E) = .05, P(E3) = P(E4) = .2,P(E5) = .06, P(E6) = .3,P(E7) = .06, and P(Eg) = .03. E1 E E E4 B A E7 Es Find the following probabilities: a) P(AC) b) P(BC) c) P(AB) d) P(AUB) e) P(ANB) f) P(A B) E6 S Es g) Are events A and B mutually exclusive? Why? 2 1. Each year CCH, Inc., a firm that provides human resources and employment law information, conducts a survey on absenteeism in the workplace. The 2007 survey found that of all unscheduled work absences, 34% are due to "personal illness", 22% for "family issues", 18% for "personal needs", 13% for "entitlement mentality", and 13% due to "stress". Consider a randomly selected employee who has an unscheduled work absence. a) List the sample points for this experiment. b) Assign reasonable probabilities to the sample points. c) What is the probability that the absence is due to something other than "personal illness"? 2. In a recent survey conducted by the International Nanny Association, 4,176 nannies were placed in a job in a given year. Only 24 of the nannies placed were men. Find the probability that a randomly selected nanny who was placed during the last year is a male nanny (a "mannie"). 1