Ans:
Given that
P(before noon)=0.80
P(after noon)=1-0.80=0.20
P(regular/before noon)=0.90
P(decaf/before noon)=0.10
P(decaf/after noon)=0.35
a)
P(decaf)=P(decaf/before noon)*P(before noon)+P(decaf/after noon)*P(after noon)
=0.1*0.80+0.35*0.20
=0.08+0.07
=0.15
b)
P(after noon/decaf)=P(decaf/after noon)*P(after noon)/P(decaf)
=0.35*0.20/0.15
=0.467
c)
P(decaf and before noon)=P(decaf/before noon)*P(before noon)=0.1*0.8=0.08
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