M118 Weeks 4 & 5

M118 Weeks 4 & 5 - PROBABI LI TY THEORY - THE RULES...

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1.)  0  1.)  0    Pr[anything]    Pr[anything]   1  1 2.)  Pr[S] = 1.0, Pr[ 2.)  Pr[S] = 1.0, Pr[ φ φ ] = 0.0 ] = 0.0 3.)  Pr[E] = sum of pr’s of outcomes in E 3.)  Pr[E] = sum of pr’s of outcomes in E 4.)  Pr[E’] = 1.0 - Pr[E] 4.)  Pr[E’] = 1.0 - Pr[E] * 5.)  If ELO, then Pr[E] = n(E)/n(S) 5.)  If ELO, then Pr[E] = n(E)/n(S) 6.) Pr[A  6.) Pr[A   B] = Pr[A]+Pr[B]-Pr[A   B] = Pr[A]+Pr[B]-Pr[A   B]   B]  7.) If A, B, and C are pairwise disjoint 7.) If A, B, and C are pairwise disjoint               events in S, then  events in S, then                Pr[A or B or C] = Pr[A]+Pr[B]+Pr[C] Pr[A or B or C] = Pr[A]+Pr[B]+Pr[C] PROBABILITY THEORY - THE RULES
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EG1) A sample space S has two events, A and B. If Pr[A] = 0.5, Pr[B] = 0.35, and Pr[A B] = 0.7, find… a.) Pr[A’ B’] b.) Pr[A B ] c.) Pr[A B’ ]
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EG2) A sample space S has three events, A, B, and C. If Pr[A] = 0.4, Pr[B] = 0.6, Pr[C] = 0.6, Pr[A B] = 0.7, Pr [A C] = 0.8, Pr[B C] = 0.3, and Pr[A B C] = 0.1, find…. a.) Pr[ A B ] d.) Pr[ A B’ C ] b.) Pr[ A C ] e.) Pr [ A’ B’ C’ ] c.) Pr[ B C ] f.) Pr [ A’ B’ C ]
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EG3) A sample space S has three events, A, B, and C, and it is true that A (B C) = . If Pr[A] = 0.4, Pr[B] = 0.35, Pr[C] = 0.25, and Pr [ A’ B’ C’ ] = 0.2, find…. a.) Pr[ C’ ] b.) Pr[ B C ] c.) Pr[ B C ] d.) Pr[ B’ C’ ]
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EG4) A sample space S = { O 1 , O 2 , O 3 , O 4 , O 5 , O 6 }, with w 1 = 0.10, w 2 = w 3 = 0.15, w 4 = 0.05, and w 5 = .30. If the event E = { O 2 , O 3 , O 6 }, and F = { O 1 , O 2 , O 4 , O 6 }, find a.) Pr [ E ] b.) Pr [ E F’ ] c.) Pr [ (E F)’ ]
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EG5) A survey of students returning from Spring Break in Florida revealed the following information: 35% got arrested 45% have no memory of the week 55% took a wrong turn and ended up in Iowa 15% got arrested and have no memory of the week 20% got arrested and ended up in Iowa 25% have no memory of the week and ended up in Iowa 10% had all three of these things happen to them a.) What proportion of the students got arrested but did not end up in IA? b.) What proportion of the students had exactly two of the three things above happen to them? c.) What proportion of the students had none of these things happen?
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EG6) After graduation, you get a job working for Pepsi. As part of your job, you must select a cow to be used in a new commercial. From past experience, you have the following information at your disposal: Event Pr[Event] a.) Pr [ something wrong ] OK 0.70 b.) Pr [ wrong weight ] too heavy (W 1 ) 0.14 c.) Pr [ wrong design ] too thin (W 2 ) 0.10 d.) Pr [ correct weight ] too many spots (D 1 ) 0.09 e.) Pr [ wrong weight or design ] too few spots (D 2 ) 0.04 f.) Pr [ wrong weight and design ] If a cow is randomly selected from among those available, find…. .
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M118 Weeks 4 & 5 - PROBABI LI TY THEORY - THE RULES...

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