PART 1(3 pages)Discuss the current financial health and the future projection on the financial sustainability of Medicare. Propose initiatives that the government might take as possibilities to prese
If E and F are independent events with P(E)=23 and P(F)=25 , then P(E and F)= (Round your answer to the nearest thousandth.)
For the spinner shown, on which all sections have equal area, let E be the event “get a number higher than 5” and F be the event “get an odd number.”
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Answer the following questions, rounding your answers to three decimal places.
What is P(E∣F) ?
What is P(F∣E) ?
Are E and F independent events?
A. No
B. Yes
A study compared people who followed the American Heart Association (AHA) diet to people who followed the Mediterranean (Med) diet, with the following results.
| Disease | No Disease | Total | |
| AHA | 63 | 251 | 314 |
| Med | 27 | 273 | 300 |
| Total | 90 | 524 | 614 |
Suppose that a study participant is chosen at random. Answer the following questions.
What is the probability that the participant was diseased if he or she followed the AHA diet? Round your answer to two decimal places.
Given that the participant was found to have disease, what is the probability that he or she followed the Mediterranean diet? Round your answer to two decimal places.
A survey of adult Americans yielded the following data:
| Smoker | Non-smoker | Total | |
| Four-year degree | 22 | 24 | |
| No four-year degree | 15 | 58 | 73 |
| Total | 15 | 82 | 97 |
How many people responded to the survey?
What is the probability that a person randomly selected from among those who responded to the survey is a smoker, given that that person has a four-year degree? Round your answer to two decimal places.
What is the sample space for this experiment?
A. { Smoker, Non-smoker, Four-year degree, No four-year degree}
B. { 2, 15, 22, 58}
C. { 97}
D. { Four-year degree/Smoker, Four-year degree/Non-smoker, No four-year degree/Smoker, No four-year degree/Non-smoker}
5. A study was performed to determine whether patients experienced an adverse event within two weeks when placed on a particular new medication. The results were as follows:
| Adverse event | No adverse event | Total | |
| Treatment group | 112 | 559 | 671 |
| Control group | 52 | 298 | 350 |
| Total | 350 | 671 | 1021 |
How many people were studied altogether?
If a patient is selected at random from among those studied, what is the probability that that person was in the control group? Round your answer to two decimal places.
If a patient is selected at random from among those studied, what is the probability that that person was in the treatment group and experienced an adverse event? Round your answer to two decimal places.
If a patient is selected at random from among those studied, what is the probability that that person was in the treatment group, given that the person experienced an adverse event? Round your answer to two decimal places.
What is the sample space for this experiment?
A. 1021
B. Treatment group, Control group, Adverse event, No adverse event
C. 112, 52, 559, 298
D. Treatment group/Adverse event, Treatment group/No adverse event, Control group/Adverse event, Control group/No adverse event
Are the events “Treatment group” and “Adverse event” independent?
A. Yes
B. No
6. One week after they began taking a new medication for chronic pyrrhonism, patients were given the standard test for that awful condition, with the following results.
| Male | Female | Total | |
| Tested positive | 38 | 25 | 63 |
| Tested negative | 24 | 26 | 50 |
| Total | 62 | 51 | 113 |
How many people were tested altogether?
What is the probability that a female patient tested negative? Round your answer to two decimal places.
Were the events “tested positive” and “female” independent?
A. No
B. Yes
7. A survey of adult Americans yielded the following data:
| Smoker | Non-smoker | Total | |
| Four-year degree | 23 | 25 | |
| No four-year degree | 15 | 60 | 75 |
| Total | 15 | 85 | 100 |
How many people responded to the survey?
What is the probability that a person randomly selected from among those who responded to the survey is a smoker, given that that person has a four-year degree? Round your answer to two decimal places.
Are the events “smoker” and “four-year degree” independent?
A. Yes
B. No
8. Janice draws a card from a standard deck and places it face down on a table without looking at it. She then draws a second card. What is the probability that the first card is a spade and the second card is a heart? Round your answer to three decimal places.
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9. For a certain experiment, two independent events E and F are known to have probabilities P(E)=0.39 and P(F)=0.6 . If the experiment is performed, what is the probability that both events occur? Round your answer to three decimal places.
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