A salesperson uses three different airlines. The probabilities of switching from one airline to another in consecutive flights are shown below. If the last flight was on Delta, what is the probability that the next was on American? American Delta Southwest American 0.5 0.25 0.25 Delta 0.2 0.6 0.2 Southwest 0.3 0.3 0.4 A 0.5 B 0.2 C 0.25 D 0.6
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A salesperson uses three different airlines. The probabilities of switching from one airline to another in consecutive flights are shown below.
If the last flight was on Delta, what is the probability that the next was on American?
|
American |
Delta |
Southwest |
American |
0.5 |
0.25 |
0.25 |
Delta |
0.2 |
0.6 |
0.2 |
Southwest |
0.3 |
0.3 |
0.4 |
A |
0.5 |
|
B |
0.2 |
|
C |
0.25 |
|
D |
0.6 |
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- Alternative A1 A2 Prior Probability State of Nature S1 S2 -40 100 0.4 75 0 0.6 There is an option of paying $100 to have research done to better predict which state of nature will occur. When the true state of nature is S1, the research will accurately predict S1 60% of the time. When the true state of nature is S2, the research will accurately predict S2 80% of the time. What is the posterior probability of S2 given that the research predicts S2?Senior executives at an oil company are trying to decide whether to drill for oil in a particular field. It costs the company $750,000 to drill. The company estimates that if oil is found the estimated value will be $3,650,000. At present, the company believes that there is a 48% chance that the field actually contains oil. Before drilling, the company can hire an expert at a cost of $75,000 to perform tests to make a prediction of whether oil is present. Based on a similar test, the probability that the test will predict oil on the field is 0.55. The probability of actually finding oil when oil was predicted is 0.85. The probability of actually finding oil when no oil was predicted is 0.2. What is the EMV if the company hires the expert?A national survey indicated that 30% of adults conduct their banking online. It also found that 40% are under the age of 50, and that 25% are under the age of 50 and conduct their banking online. A. What percentage of adults do not conduct their banking online? B. What type of probability is the 25% mentioned above? Just write down the name of the probability. C. Construct a joint probability table showing all joint and marginal probabilities.
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- This type of analysis is most appropriate when the past is a good predictor of the future.A NY Times best-selling author wants to write a new book as either volume II of her earlier successful book or an autobiography. She believes that by writing the volume II, given her previous success, she will have a 50% chance of placing it with a major publisher where it should ultimately sell about 40,000 copies. However, the worst-case scenario, if she can’t get a major publisher to take it, then she thinks there is 80% chance of placing it with a smaller publisher, with sales of 30,000 copies. On the other hand, if she writes an autobiography, considering the potential interest in her journey as successful writer, she thinks there will be 40% chance of placing it with a major publisher, and it should result in ultimate sales of about 50,000 copies. If she can’t get a major publisher to take it, the worst-case scenario, she thinks there is a 50% chance of placing it with a smaller publisher, with ultimate sales of 35,000 copies. Construct a decision tree to help this author…A recent 10-year study conducted by a research team at the Great Falls Medical School was conducted to assess how age, systolic blood pressure, and smoking relate to the risk of strokes. Assume that the following data are from a portion of this study. Risk is interpreted as the probability (times 100) that the patient will have a stroke over the next 10-year period. For the smoking variable, define a dummy variable with 1 indicating a smoker and 0 indicating a nonsmoker. The data is provided below: Risk of Strokes Age Systolic Blood Pressure Smoker 10 59 156 0 25 65 163 0 12 60 158 0 57 86 177 1 28 59 196 0 50 76 189 1 17 57 159 1 34 78 120 1 37 80 135 1 15 78 98 0 22 71 152 1 39 70 173 1 17 67 135 0 48 77 209 1 18 60 199 0 36 82 119 1 10 66 166 0 34 80 125 1 4 62 117 0 38 59…