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A construction firm is currently working on two different buildings. Let denote the event that the ith building is completed by the contract date. Use the operations of union, intersection, and complementation to describe each of the following events in terms of A1 and A2and draw a Venn diagram, and shade the region corresponding to each one. 1. At least one building is completed by the contract date Both buildings are completed by the contract date Only the first building is completed by the contract date Exactly one building is completed by the contract date a. b. c. d.

math   Statistics-And-Probability   
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Answer #1

Solution for sub-part of a) and b) :-

Solution A 1 Event ot buildling 1 Completed b Conthect date A2 Event of buildin4 2 completed b conat date. S Sample Space Cset ot ai possible outcomes) a.→RE Least one bu iclind ls completed ba the Contract date. A1 UA2 event hat at least me building is completed b Contiact date. b. → Both bui dings emnec iCompleted by Conthact date A1nA2 event that both buildings contna t date. one completed 5 A venn dianam C 。te :-Sha dedaegion叼represents th e desired event)

Solution for sub-part of c) and d) :-

C, → Onlǎ fiast bui bling IS completed 6J the conthat olate A1 nA - event A1 excludling A2 2 venn cianam d→ Exactly one buildanats completed b the Contact date Hene we ave too b uildiną s So aue OD ent (A1 excluoling AA excluoing A. excluding Ao) 2 Venn dliu Note Shuded region repnesents he desired event)

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