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# Pre-Cal 40S Slides May 26, 2008

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Conditional probability and medical testing.

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### Pre-Cal 40S Slides May 26, 2008

1. 1. Medical Testing or Why are doctors so darn cagey?!? Let me check your sugar. by ﬂickr user Cataract eye
2. 2. Identify the events as: dependent mutually exclusive Drag'n Drop Baby! independent 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. independent mutually exclusive b. One card - a red card or a king - is randomly drawn from a deck of cards. independent not mutually exclusive c. A class president and a class treasurer are randomly selected from a group of 16 students. dependent mutually exclusive d. One card - a red king or a black queen - is randomly drawn from a deck of cards. mutually exclusive independent e. Rolling two dice and getting an even sum or a double. independent not mutually exclusive
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. 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)
5. 5. 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
6. 6. 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?
7. 7. 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?
8. 8. 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?
9. 9. 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?