Class 33
Probability
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Homework Check
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Assignment:
Chapter 7 – Exercise 7.68, 7.69 and 7.70
Reading:
Chapter 7 – p. 238-247
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Suggested Answer
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Suggested Answer
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Suggested Answer
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Suggested Answer
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Suggested Answer
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Do Now – 2Way Table
Question:
1. P ( attended seminar and increased sales attended seminar)
2. P ( NOT attended seminar and increased sales NOT attended
seminar)
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Do Now- Simulation
Shooting Baskets
• Mr. Myer shot free throws at a 70% this
season.
• How likely is it that he would make 7 shots
in a row out of 10 shots? (Simulate 15
repetitions)
• Mr. Jameson shoots free throws at a 54%
rate.
• How often would he make 7 in a row out of
10 shots? (Simulate 15 repetitions)
Use Tree Diagram
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Use Tree Diagram
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Use Tree Diagram and Random
Number to do simulation
Question:
Morris’s kidneys have failed and he is awaiting a kidney
transplant. His doctor gives him this information for
patients in his condition: 90% survive the transplant
operation, and 10% die. The transplant succeeds in 60% of
those who survive, and the other 40% must return to kidney
dialysis. The proportions who survive for at least five years
are 70% for those with a new kidney and 50% for those who
return to dialysis. Morris wants to know the probability that
he will survive for at least 5 years.
Draw a Tree Diagram
Use Tree diagram to do simulation
Step 1: Construct a tree diagram
Survive
Survive
Die
0.3
0.9
Dialysis
0.4
0.1
0.7
New
Kidney
0.6
Survive
Die
0.5
0.5
Die
Use Tree diagram to do simulation
Step 2: Assign digits to outcome
Stage 1:
0 = die
1,2,3,4,5,6,7,8,9 = survive
Stage 2:
0, 1, 2, 3, 4, 5 = transplant succeeds
6, 7, 8, 9 = return to dialysis
Stage 3 with new kidney:
0, 1, 2, 3, 4, 5, 6 = survive for 5 years
7, 8, 9 = die
Stage 3 with dialysis:
0, 1, 2, 3, 4 = survive for 5 years
5, 6, 7, 8, 9 = die
Use Tree diagram to do simulation
Step 3: Use random number table to do simulations of
several repetitions to determine the estimated
probability of “survive five years”, each arranged
vertically
For example: random number: 17138 27584 252
Repetition1
Repetition 2
Repetition 3
Repetition 4
Stage 1
1 -> Survive
3 -> Survive
7 -> Survive
4 -> Survive
Stage 2
7 -> return to
dialysis
8 -> return to
dialysis
5 -> New Kidney
2 -> New Kidney
Stage 3
1 -> Survive
2 -> Survive
8 -> Die
5 -> Survive
Morris survives five years in 3 of the 4 repetitions.
The estimated probability = 3/ 4
7.7 Flawed Intuitive Judgments
about Probability
Confusion of the Inverse
Example: Diagnostic Testing
Confuse the conditional probability “have the disease”
given “a positive test result” -- P(Disease | Positive),
with the conditional probability of “a positive test result”
given “have the disease” -- P(Positive | Disease), also
known as the sensitivity of the test.
Often forget to incorporate the base rate for a disease.
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Specific People versus
Random Individuals
The chance that your marriage will end in divorce is 50%.
Does this statement apply to you personally?
If you have had a terrific marriage for 30 years, your
probability of ending in divorce is surely less than 50%.
Two correct ways to express the aggregate divorce statistics:
• In long run, about 50% of marriages end in divorce.
• At the beginning of a randomly selected marriage,
the probability it will end in divorce is about 0.50.
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Coincidences
A coincidence is a surprising concurrence of events,
perceived as meaningfully related, with no apparent
causal connection.
Example 7.33 Winning the Lottery Twice
In 1986, Ms. Adams won the NJ lottery twice in a short time
period. NYT claimed odds of one person winning the top prize
twice were about 1 in 17 trillion. Then in 1988, Mr. Humphries
won the PA lottery twice.
1 in 17 trillion = probability that a specific individual who
plays the lottery exactly twice will win both times.
Millions of people play the lottery. It is not surprising
that someone, somewhere, someday would win twice.
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The Gambler’s Fallacy
The gambler’s fallacy is the misperception of
applying a long-run frequency in the short-run.
• Primarily applies to independent events.
• Independent chance events have no memory.
Example:
Making ten bad gambles in a row doesn’t change
the probability that the next gamble will also be bad.
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Homework
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Assignment:
Chapter 7 – Exercise 7.83, 7.85 and 7.89
Reading:
Chapter 7 – p. 238-247
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