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Tree Diagram
Medical Example
Quality Control Example
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A
tree diagram helps us represent the various
events and their associated probabilities. The
various outcomes of each experiment are
represented as branches emanating from a point.
Each branch is labeled with the probability of the
associated outcome.
For example:
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We
represent experiments performed one after
another by stringing together diagrams of the sort
given in the previous slide. The probabilities for
the second set of branches are conditional
probabilities given the outcome from which the
branches are emanating.
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For
example:
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The
reliability of a skin test for active pulmonary
tuberculosis (TB) is as follows: Of people with TB,
98% have a positive reaction and 2% have a
negative reaction; of people free of TB, 99% have a
negative reaction and 1% have a positive reaction.
From a large population of which 2 per 10,000
persons have TB, a person is selected at random
and given a skin test, which turns out positive.
What is the probability that the person has active
TB?
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Make
a tree diagram using:
Pr(TB) = 2/10000 = .0002,
Pr(not TB) = 1 - .0002 = .9998,
Pr(TB|Neg) = .98,
Pr(TB|POS) = .02,
PR(NEG|not TB) = .99 and
PR(POS|not TB) = .01.
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Pr(TB  POS)
.000196
So Pr(TB|POS) =

 .02.
Pr(POS)
.000196  .009998
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A
box contains 5 good light
bulbs and 2 defective ones.
Bulbs are selected one at a
time (without replacement)
until a good bulb is found.
Find the probability that the
number of bulbs selected is (i)
1, (ii) 2, (iii) 3.
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For
the first draw, a bulb selected at random is
good (G) with probability 5/7
For the first draw, a bulb selected at random is
defective (D) with probability 2/7
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If
the first bulb was good, the
activity stops.
If the first bulb was defective, then
the second selection is good with
probability 5/6 and defective with
probability 1/6.
If the second selection was good,
the activity stops.
If it was defective, then the third
selection is good with probability 1.
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The
tree diagram is:
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(i ) Pr(1) 
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2 5 5
(ii ) Pr(2)   
7 6 21
2 1
1
(iii ) Pr(3)   1 
7 6
21
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Tree diagrams provide a useful device for
determining probabilities of combined outcomes in
a sequence of experiments.

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