Died from Cancer Did Not Die from Cancer
Never smoked cigars 620 123,094
Former cigar smoker 54 7,161
Current cigar smoker 193 5,839
(a) If an individual is randomly selected from this study, what is the probability that he died from cancer?
(b) If an individual is randomly selected from this study, what is the probability that he was a current cigar smoker?
(c) If an individual is randomly selected from this study, what is the probability that he died from cancer and was a current cigar smoker?
(d) If an individual is randomly selected from this study, what is the probability that he died from cancer or was a current cigar smoker?
The correct answer and explanation is :
Given the data provided, we can calculate the following probabilities:
(a) Probability that an individual died from cancer:
Total number of individuals:
- Never smoked cigars: 620 + 123,094 = 123,714
- Former cigar smokers: 54 + 7,161 = 7,215
- Current cigar smokers: 193 + 5,839 = 6,032
Grand total: 123,714 + 7,215 + 6,032 = 136,961
Total number of deaths from cancer:
- Never smoked cigars: 620
- Former cigar smokers: 54
- Current cigar smokers: 193
Total cancer deaths: 620 + 54 + 193 = 867
Therefore, the probability is 867 / 136,961 ≈ 0.0063 or 0.63%.
(b) Probability that an individual was a current cigar smoker:
Total number of current cigar smokers:
- Current cigar smokers: 193 + 5,839 = 6,032
Probability: 6,032 / 136,961 ≈ 0.044 or 4.4%.
(c) Probability that an individual died from cancer and was a current cigar smoker:
Number of current cigar smokers who died from cancer:
- Current cigar smokers who died from cancer: 193
Probability: 193 / 136,961 ≈ 0.0014 or 0.14%.
(d) Probability that an individual died from cancer or was a current cigar smoker:
Using the formula P(A or B) = P(A) + P(B) – P(A and B):
- P(Death from cancer): 867 / 136,961 ≈ 0.0063
- P(Current cigar smoker): 6,032 / 136,961 ≈ 0.044
- P(Death from cancer and current cigar smoker): 193 / 136,961 ≈ 0.0014
Therefore, the combined probability is:
0.0063 + 0.044 – 0.0014 = 0.0499 or 4.99%.
Explanation:
These calculations provide insights into the relationships between smoking habits and cancer mortality. Notably, the probability that an individual died from cancer (0.63%) is relatively low, which might be expected in a general population sample. However, the probability that an individual was a current cigar smoker (4.4%) is higher than the cancer death rate, suggesting that smoking is a prevalent behavior within this group. Moreover, the probability that an individual both died from cancer and was a current cigar smoker (0.14%) reflects the increased risk associated with smoking. Finally, the combined probability (4.99%) indicates the proportion of individuals who either died from cancer or were current cigar smokers, highlighting the significant impact of smoking on cancer mortality.
These findings underscore the strong association between tobacco use and cancer, reinforcing the importance of smoking cessation programs and public health initiatives aimed at reducing tobacco consumption.