In an earlier example you constructed a decision tree showing event in order to calculate the probabilities of three siblings by gender
You were asked to calculate the probabilities of siblings with different numbers if siblings and genders
This time you will have to construct a tree calculating the probabilities of a mother giving birth to two consequtive sets of twins after two different pregnancies.
Construct the decision tree and answer the following questions
1 - What is the probability of having two boy and two girls?
2 - What is the probability of having twin boys followed by twin girls?
3 - What is the probability of a girl having two or more brothers
4 - What is the probability of having both boys and girls amongst your two sets of twins?
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Problem 2
Decision Trees
In an earlier example , you explored a decision tree for a business trying to do a product rollout by December
For this example you are going to examine another situation
In this case a company needs to make a decision about their manufacturing facility
They can
A) not expand their business at all
B) expand their operations here in the US, or
C) expand their operations by outsourcing to China
For each scenario, there are three possible events that can occur
1) Business conditions can remain unchanged, with salkes and revenue remaining unchanged
2) Business conditions can improve, allowing more growth
3) or Business conditions can worsen reducing sales and revenues
The business currently makes about $200 million dollars a year.
If business conditions improve, revenues would increase by 50%
If business conditions worsen revenues would drop by 50%
Outsourcing would cost the company about $100 million the first year to set up a manufacturing facility overseas, but would save about 20%/year (i.e., savings equal to 20% of revenue), thus increasing net earnings
Expanding locally would increase costs by $50million the first year
If neither expansion nor outsourcing occurs, potential increases in sales would not be achieved
If the probabilities of changes in business conditions are as noted below,
Calculate the expected payoff for each choice, A, B, or C and each of the events based on two years of earnings/costs/savings
economy unchanged 50.00% savings from outsourcing 20.00%
economy improves 20.00% cost to outsource -100
economy worsens 30.00% cost to expand -50
Represent in a decision tree
Identify the optimum choice
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Problem 3
In your readings you had an example of a project PERT chart that had durations of different steps characterized in terms of Best case duration, worse case duration, and most likely duration
For the table below,
draw a PERT network diagram
calculate the estimated duration for each activity (TE - estimated time) cumulative single tail probability table
identify the critical path based on the expected time
what is the probability of completing the project in 30 days
a m b predecessors TE variance Expected Time Critical path
A 2 5 6 - -9.00 -0.69 4.67
B 4 8 10 - -14.00 1.00 7.67 1.00
C 2 3 5 A -6.00 11.98 3.17
D 1.5 3 6 C -7.50 3.84 3.25
E 4 5 8 B -9.00 2.60 5.33
F 5 10 15 B -20.00 37.86 10.00 6.15
G 3 7 10 D -14.00 22.74 6.83
H 3.5 5 7 D -8.50 4.15 5.08
I 2 4 8 E -10.00 6.84 4.33
J 2 4 5 E -7.00 5.68 3.83
K 2 3 5 G -6.00 1.91 3.17
L 4 7 12 H,I -15.00 15.39 7.33
M 4 8 16 J,F -20.00 27.36 8.67 5.23
