Cigar Smoking The data in the following table show the association between cigar smoking and death from cancer for 139,704 men. Note: Current cigar smoker means cigar smoker at time of death.
b) If an individual is randomly selected from this study, what is the probability that he was a current cigar smoker?

Verified step by step guidance

1. Step 1: Identify the total number of men in the study by summing all the values in the table. This includes men who died from cancer and those who did not, across all smoking categories.
2. Step 2: Calculate the total number of current cigar smokers by adding the number of current cigar smokers who died from cancer to those who did not die from cancer.
3. Step 3: Use the formula for probability to find the probability that a randomly selected individual was a current cigar smoker. The formula is: \(P(\text{Current cigar smoker}) = \frac{\text{Number of current cigar smokers}}{\text{Total number of men}}\)
4. Step 4: Substitute the values found in Steps 1 and 2 into the probability formula.
5. Step 5: Simplify the fraction to express the probability, which represents the likelihood that a randomly selected man from the study was a current cigar smoker.

Key Concepts

Probability

Probability measures the likelihood of an event occurring, expressed as a number between 0 and 1. In this context, it refers to the chance that a randomly selected individual from the study is a current cigar smoker. It is calculated by dividing the number of current cigar smokers by the total number of individuals in the study.

Sample Space and Events

The sample space is the set of all possible outcomes, here all men in the study. An event is a subset of the sample space, such as being a current cigar smoker. Understanding these helps in identifying the correct numerator and denominator when calculating probabilities.

Data Categorization and Interpretation

Data is organized into categories based on cigar smoking status and cancer death outcome. Interpreting this table correctly is essential to extract relevant counts for probability calculations, ensuring the correct totals for each category and overall sample size are used.