The following table shows the number of women with breast cancer per 1,000,000 women in different age groups: Age 15-39 40-64 65+ Cases 250 2,250 4,000 As seen above, the prevalence rate [the proportion of a particular population found to be affected by a medical condition] of breast cancer for the younger group is very low compared to the older group. You can think of the prevalence rate as the prior probability a given woman has cancer in that age group. Alice (age between 15 and 39) and Elisabeth (age over 65) requested their mammograms approved by their doctors. Both of the tests turned out to be positive. The properties of the test are as follows: 90% of patients with breast cancer test positive, and 99% of patients without breast cancer test negative. Consider the data above. What are the posterior probabilities of Alice and Elisabeth having breast cancer given their test results, respectively, in percentage?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
The following table shows the number of women with breast cancer per 1,000,000 women in different age groups:
| Age | 15-39 | 40-64 | 65+ |
| Cases | 250 | 2,250 | 4,000 |
As seen above, the prevalence rate [the proportion of a particular population found to be affected by a medical condition] of breast cancer for the younger group is very low compared to the older group. You can think of the prevalence rate as the prior probability a given woman has cancer in that age group.
Alice (age between 15 and 39) and Elisabeth (age over 65) requested their mammograms approved by their doctors. Both of the tests turned out to be positive. The properties of the test are as follows: 90% of patients with breast cancer test positive, and 99% of patients without breast cancer test negative.
Consider the data above. What are the posterior probabilities of Alice and Elisabeth having breast cancer given their test results, respectively, in percentage?
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