A) If a patient is randomly selected, what is the probability that he/she had prostate cancer given that fish was never or seldom a part of the diet? Round your answer to three decimal places and include the leading zero. B) If a patient is randomly selected, what is the probability that s/he ate fish as a large part of their diet given that they had prostate cancer. Round your answer to two decimal places and include the leading zero.
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.
Medical researchers followed 6272 Swedish men for 30 years to see if there was any association between the amount of fish in their diet and prostate cancer. (“Fatty Fish Consumption and Risk of Prostate Cancer,” Lancet, June 2001). A summary of the data is given in the table below.
| Fish Consumption | No Prostate Cancers | Prostate Cancers |
| Never/Seldom | 110 | 14 |
| Small part of diet | 2420 | 201 |
| Moderate part of diet | 2769 | 209 |
| Large part of diet | 507 | 42 |
A) If a patient is randomly selected, what is the probability that he/she had prostate cancer given that fish was never or seldom a part of the diet? Round your answer to three decimal places and include the leading zero.
B) If a patient is randomly selected, what is the probability that s/he ate fish as a large part of their diet given that they had prostate cancer. Round your answer to two decimal places and include the leading zero.
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