Assume that the probability of any subinterval I of [-1, 2] is proportional to its length
P(I)=k⋅length(I) If we let I=[−2,1], then we must have
1=P(S)=P([−2,1])=k⋅length([−2,1])=k⋅3k=31P[A]=31length([−1,0))=31⋅1=31
∣x−0.5∣<0.5=>−0.5<x−0.5<0.5=>0<x<1
P[B]=31length((0,1))=31⋅1=31
P[C]=31length((0.75,2))=31⋅1.25=125
P[A∣B]=P[B]P[A∩B]=0
P[B∩C]=31length((0.75,1))=31⋅0.25=121
P[B∣C]=P[C]P[B∩C]=125121=51
P[CC]=1−125=127
P[A∩CC]=31length([−1,0))=31⋅1=31
P[A∣CC]=P[CC]P[A∩CC]=12731=74
P[B∩CC]=31length(0,0.75])=31⋅0.75=41
P[B∣CC]=P[CC]P[B∩CC]=12741=73
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