i. Suppose at a particular coffee shop, 80% of the cups of coffee are sold befor

Question

i. Suppose at a particular coffee shop, 80% of the cups of coffee are sold before noon. If the coffee is purchased before noon, there's a 90% chance it's regular (and a 10% chance it's decaf). If the coffee is purchased after noon, there's a 35% chance it's decaf. (a) What's the probability that a randomly selected coffee purchase is decaf? (b) If we learn that a certain purchased cup of coffee was decaf, what's the probability that the purchase was made after noon? (c) Find the probability th at a randomly selected coffee purchase is for decaf coffee before noon.

Explanation / Answer

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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