Venn and Tree Diagrams
P(A) =.4 P(B) = .7 P(A  B) =.2
P(C) = .3
P(A  B) =
P(A  B  C) =
P(A’) =
P(C’) =
P(B’) =
P(B’ C’) =
P(A  B’) =
P((A  B’)  C’) =
P(A  B’) =
P(C  B) =
P(A’  B’) =
P(C’  B’) =
P(A’  B’) =
P((C  B’)  A’) =
P(A’  B) =
P((A  B) | C) =
P(A | B) =
P(A | C’) =
P(A  C) =.15
P(C  B) =.2
P(A  B  C) = .1
You are a manager for a candy company and are responsible for packaging all the bags of Holloween candy.
You have 2 bagging machines, Machine A tends to make an error (the bag doesn’t completely close/seal) 2%
of the time. Machine B tends to make the same error 10% of the time. Obviously you would prefer to just
always use Machine A, however, Holloween is a very busy season and in order to fill all the orders, both
machines must be used. So you run 65% of your candy through machine A and the rest through. Machine B.
This means machine A is running 24 ours a day, and Machine B is running just enough to meet production
goals.
What percent of your candy bags will be defective?
If you find a defective bag, what is the probability it came from machine A? What is the probability it came
from machine B?
Walmart requires that no more than 4% of the bags sent to their stores can be defective What % of the time
would you need to run machine A in order to meet this requirement and still maximize production?
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