# ProbSetTwo - Rensselaer Electrical Computer and Systems...

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Rensselaer Electrical, Computer, and Systems Engineering Department ECSE 4500 Probability for Engineering Applications PS#2 Solutions February 12, 2010 1. (1.13) (a) For simplicity we make the following associations: cat =1 ,dog =2 , goat =3 ,p ig =4 . Then the f eld F consists of 16 events: { 1 } , { 2 } , { 3 } , { 4 } , { 1 , 2 } , { 1 , 3 } , { 1 , 4 } , { 2 , 3 } , { 2 , 4 } , { 3 , 4 } , { 1 , 2 , 4 } , { 1 , 2 , 3 } , { 1 , 3 , 4 } , { 2 , 3 , 4 } , { 1 , 2 , 3 , 4 } ,and φ .No tetha t { 1 , 2 } = { 1 } S { 2 } ,and P [ { 1 , 2 } ]= P [ { 1 } ]+ P [ { 2 } ] P [ { 1 } T { 2 } ] where P [ { 1 } T { 2 } ]=0 .Bu t P [ { 2 } ]=0 . 5 , therefore P [ { 1 } ]=0 . 9 0 . 5=0 . 4 . Similarly, P [ { 3 , 4 } ]=0 . 1= P [ { 4 } ]+ P [ { 3 } ] =0 . 05 + P [ { 3 } ] Therefore P [ { 3 } ]=0 . 05 , P [ { 2 } ]=0 . 5 , P [ { 4 } ]=0 . 05 ,and P [ { 1 } ]=0 . 4 .F r omt h e s e probabilities we can compute all other probabilities using P [ A S B ]= P

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ProbSetTwo - Rensselaer Electrical Computer and Systems...

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