Pre-Cal 40S Slides January 10, 2008

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More or independence, dependence, mutual exclusivity. Conditional probability and medical testing.

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Pre-Cal 40S Slides January 10, 2008

  1. 1. Risk is when an outcome’s probability is known. Uncertainty is when an outcome’s probability is unknown.
  2. 2. ` Phone Numbers A computer is used to generate random telephone numbers. Of the numbers generated and in service, 56 are unlisted and 144 are listed in the telephone directory. If one of these telephone numbers is randomly selected, what is the probability that it is unlisted?
  3. 3. Testing for independence ... 30% of seniors get the flu every year. 50% of seniors get a flu shot annually. 10% of seniors who get the flu shot also get the flu. Are getting a flu shot and getting the flu independent events?
  4. 4. Testing for independence ... 30% of seniors get the flu every year. 50% of seniors get a flu shot annually. 10% of seniors who get the flu shot also get the flu. Are getting a flu shot and getting the flu independent events?
  5. 5. Testing for independence ... 30% of seniors get the flu every year. 50% of seniors get a flu shot annually. 10% of seniors who get the flu shot also get the flu. Are getting a flu shot and getting the flu independent events?
  6. 6. Testing for independence ... 30% of seniors get the flu every year. 50% of seniors get a flu shot annually. 10% of seniors who get the flu shot also get the flu. Are getting a flu shot and getting the flu independent events?
  7. 7. Probabilities involving quot;andquot; and quot;orquot; A.K.A quot;The Addition Rulequot;... The addition rule is a result used to determine the probability that event A or event B occurs or both occur. The result is often written as follows, using set notation: P(A or B) = P(A∪B) = P(A)+P(B) - P(A∩B) where: P(A) = probability that event A occurs P(B) = probability that event B occurs P(A U B) = probability that event A or event B occurs P(A ∩ B) = probability that event A and event B both occur P(A and B) = P(A∩B) = P(A)*P(B)
  8. 8. Chad has arranged to meet his girlfriend, Stephanie, either in the library or in the student lounge. The probability that he meets her in the lounge is 1/3, and the probability that he meets her in the library is 2/9. a. What is the probability that he meets her in the library or lounge? b. What is the probability that he does not meet her at all?
  9. 9. Identify the events as independent, dependent, mutually exclusive, or not mutually exclusive. a. A bag contains four red and seven black marbles. The event is randomly selecting a red marble from the bag, returning it to the bag, and then randomly selecting another red marble from the bag. b. One card - a red card or a king - is randomly drawn from a deck of cards. c. A class president and a class treasurer are randomly selected from a group of 16 students. d. One card - a red king or a black queen - is randomly drawn from a deck of cards. e. Rolling two dice and getting an even sum or a double.
  10. 10. Suppose a test for cancer is known to be 98% accurate. This means that the outcome of the test is correct 98% of the time. Suppose that 0.5% of the population have cancer. What is the probability that a person who tests positive for cancer has cancer? Suppose 1 000 000 randomly selected people are tested. There are four possibilities: • A person with cancer tests positive • A person with cancer tests negative • A person without cancer tests positive • A person without cancer tests negative
  11. 11. Suppose a test for cancer is known to be 98% accurate. This means that the outcome of the test is correct 98% of the time. Suppose that 0.5% of the population have cancer. What is the probability that a person who tests positive for cancer has cancer? (1) (a)How many of the people tested have cancer? (b) How many do not have cancer? (2) Assume the test is 98% accurate when the result is positive. (a) How many people with cancer will test positive? (b) How many people with cancer will test negative? (3) Assume the test is 98% accurate when the result is negative. (a) How many people without cancer will test positive? (b) How many people without cancer will test negative? (4) (a) How many people tested positive for cancer? (b) How many of these people have cancer? (c) What is the probability that a person who tests positive for cancer has cancer?
  12. 12. Suppose a test for cancer is known to be 98% accurate. This means that the outcome of the test is correct 98% of the time. Suppose that 0.5% of the population have cancer. What is the probability that a person who tests positive for cancer has cancer?
  13. 13. Suppose a test for industrial disease is known to be 99% accurate. This means that the outcome of the test is correct 99% of the time. Suppose that 1% of the population has industrial disease. What is the probability that a person who tests positive has industrial disease?

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