Post on 03-Jan-2016
Probability
Class 33
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Homework Check• 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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Do Now – 2Way Table
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Question: 1. P ( attended seminar and increased sales attended seminar)
2. P ( NOT attended seminar and increased sales NOT attended seminar)
Do Now- SimulationShooting 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
0.9
0.6
0.1 0.5
0.4
0.7
0.5
0.3Survive
Survive
New Kidney
Survive
Die
Die
Dialysis
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 dialysisStage 3 with new kidney: 0, 1, 2, 3, 4, 5, 6 = survive for 5 years 7, 8, 9 = dieStage 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 verticallyFor 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
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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
• 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.
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%.
The chance that your marriage will end in divorce is 50%.
Two correct ways to express the aggregate divorce statistics:
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Coincidences
Example 7.33 Winning the Lottery Twice
A coincidence is a surprising concurrence of events, perceived as meaningfully related, with no apparent causal connection.
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
• 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.
The gambler’s fallacy is the misperception of applying a long-run frequency in the short-run.
Homework• Assignment:• Chapter 7 – Exercise 7.83, 7.85 and 7.89• Reading:• Chapter 7 – p. 238-247
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