1. Probability Class 33 1

2. Homework Check Assignment: Chapter 7 – Exercise 7.68, 7.69 and 7.70 Reading: Chapter 7 – p. 238-247 2

3. Suggested Answer 3

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8. Do Now – 2Way Table 8 Question: 1.P ( attended seminar and increased sales attended seminar) 2. P ( NOT attended seminar and increased sales NOT attended seminar)

9. 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)

10. Use Tree Diagram 10

11. Use Tree Diagram 11

12. 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

13. 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 0.3 Survive New Kidney Survive Die Dialysis Die

14. 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

15. 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 Repetition1Repetition 2Repetition 3Repetition 4 Stage 11 -> Survive3 -> Survive7 -> Survive4 -> Survive Stage 27 -> return to dialysis 8 -> return to dialysis 5 -> New Kidney2 -> New Kidney Stage 31 -> Survive2 -> Survive8 -> Die5 -> Survive Morris survives five years in 3 of the 4 repetitions. The estimated probability = 3/ 4

16. 16 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.

17. 17 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:

18. 18 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.

19. 19 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.

20. Homework Assignment: Chapter 7 – Exercise 7.83, 7.85 and 7.89 Reading: Chapter 7 – p. 238-247 20