When women turn 40, their physicians typically remind them that it is time to undergo mammography screening for breast cancer. The data in the following table are based on 100,000 U.S. women, ages 40 to 50, who participated in mammography screening. Assume the sample is representative of this population and note that medical tests can be positive or negative, regardless of whether or not a patient has the condition. Positive Mammogram Negative Mammogram Breast Cancer 720 80 No Breast Cancer 6944 92,256 Answer questions 1-8 and compare your answers with your group. For a woman, age 40-50, selected at random, find the probability that she: 1. has breast cancer? does not have breast cancer? 2. has a positive mammogram? has a negative mammogram? 3. has a positive mammogram, given that she has breast cancer? This is known as the sensitivity of the test. 4. has a negative mammogram, given that she does not have breast cancer? This is known as the specificity of the test.

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Chapter1: Combinatorial Analysis
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PART 1. Conditional Probability (which is defined on page 281).
Definition: Conditional Probability
The conditional probability of F given E, read P(FIE), is the probability that F occurs,
given that E is known to have occurred.
P(E and F) N(E and F)
P(F|E) =
P(E)
N(E)
ACTIVITY:
When women turn 40, their physicians typically remind them that it is time to
undergo mammography screening for breast cancer. The data in the following
table are based on 100,000 U.S. women, ages 40 to 50, who participated in
mammography screening. Assume the sample is representative of this
population and note that medical tests can be positive or negative, regardless of
whether or not a patient has the condition.
Positive Mammogram
Negative Mammogram
Breast Cancer
720
80
No Breast Cancer
6944
92,256
Answer questions 1-8 and compare your answers with your group. For a
woman, age 40-50, selected at random, find the probability that she:
1. has breast cancer? does not have breast cancer?
2. has a positive mammogram? has a negative mammogram?
3. has a positive mammogram, given that she has breast cancer?
This is known as the sensitivity of the test.
4. has a negative mammogram, given that she does not have breast cancer?
This is known as the specificity of the test.
Transcribed Image Text:PART 1. Conditional Probability (which is defined on page 281). Definition: Conditional Probability The conditional probability of F given E, read P(FIE), is the probability that F occurs, given that E is known to have occurred. P(E and F) N(E and F) P(F|E) = P(E) N(E) ACTIVITY: When women turn 40, their physicians typically remind them that it is time to undergo mammography screening for breast cancer. The data in the following table are based on 100,000 U.S. women, ages 40 to 50, who participated in mammography screening. Assume the sample is representative of this population and note that medical tests can be positive or negative, regardless of whether or not a patient has the condition. Positive Mammogram Negative Mammogram Breast Cancer 720 80 No Breast Cancer 6944 92,256 Answer questions 1-8 and compare your answers with your group. For a woman, age 40-50, selected at random, find the probability that she: 1. has breast cancer? does not have breast cancer? 2. has a positive mammogram? has a negative mammogram? 3. has a positive mammogram, given that she has breast cancer? This is known as the sensitivity of the test. 4. has a negative mammogram, given that she does not have breast cancer? This is known as the specificity of the test.
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