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If an individual is randomly selected from this study, what is the probability that he died from cancer or was a current cigar smoker?
Died from Cancer
Never smoked cigars=777
Former cigar smoker=88
Current cigar smoker=108
Did Not Die from Cancer
Never smoked cigars=121,312
Former cigar smoker=6,168
Current cigar smoker=9,684
To find the probability that an individual randomly selected from the study died from cancer or was a current cigar smoker, we need to add the probabilities of each event happening.
The probability of dying from cancer is (777 + 88) / (777 + 88 + 121,312 + 6,168 + 9,684) = 865 / 137,029.
The probability of being a current cigar smoker is (108 + 9,684) / (777 + 88 + 121,312 + 6,168 + 9,684) = 9,792 / 137,029.
To find the probability of either event happening, we add these probabilities together:
(865 + 9,792) / 137,029 = 10,657 / 137,029.
So, the probability that an individual randomly selected from this study died from cancer or was a current cigar smoker is 10,657 / 137,029.
Use the General Addition Rule to find the probability. The rule states that for any two events E and F, P(E or F)=P(E)+P(F)-P(E and F).
To find the probability that an individual randomly selected from the study died from cancer or was a current cigar smoker using the General Addition Rule, we need to find the probabilities of each event individually and subtract the probability of both events happening.
The probability of dying from cancer is (777 + 88) / (777 + 88 + 121,312 + 6,168 + 9,684) = 865 / 137,029.
The probability of being a current cigar smoker is (108 + 9,684) / (777 + 88 + 121,312 + 6,168 + 9,684) = 9,792 / 137,029.
The probability of both dying from cancer and being a current cigar smoker is 88 / (777 + 88 + 121,312 + 6,168 + 9,684) = 88 / 137,029.
Using the General Addition Rule: P(Died from Cancer or Current Cigar Smoker) = P(Died from Cancer) + P(Current Cigar Smoker) - P(Died from Cancer and Current Cigar Smoker)
= 865 / 137,029 + 9,792 / 137,029 - 88 / 137,029
= (865 + 9,792 - 88) / 137,029
= 10,569 / 137,029.
So, the probability that an individual randomly selected from this study died from cancer or was a current cigar smoker, using the General Addition Rule, is 10,569 / 137,029.
To find the probability that an individual randomly selected from the study died from cancer or was a current cigar smoker, we need to calculate the total number of individuals in these two categories, as well as the total number of individuals in the study.
Total individuals who died from cancer = 777 (Never smoked cigars) + 88 (Former cigar smoker) + 108 (Current cigar smoker) = 973
Total individuals who did not die from cancer = 121,312 (Never smoked cigars) + 6,168 (Former cigar smoker) + 9,684 (Current cigar smoker) = 137,164
Total individuals in the study = Total individuals who died from cancer + Total individuals who did not die from cancer = 973 + 137,164 = 138,137
Therefore, the probability that an individual randomly selected from the study died from cancer or was a current cigar smoker is:
Probability = (Total individuals who died from cancer + Total individuals who were current cigar smokers) / Total individuals in the study
= (973 + 108) / 138,137
= 1,081 / 138,137
≈ 0.0078 or 0.78% (rounded to two decimal places)
So, the probability is approximately 0.78%.
To find the probability that an individual randomly selected from this study died from cancer or was a current cigar smoker, we need to calculate the total number of individuals who fit either of these categories, and then divide it by the total number of individuals in the study.
Let's calculate the total number of individuals who died from cancer or were current cigar smokers:
Number of individuals who died from cancer = Never smoked cigars + Former cigar smoker + Current cigar smoker
= 777 + 88 + 108
= 973
Number of individuals who were current cigar smokers = Current cigar smoker
= 108
Now, let's calculate the total number of individuals in the study:
Total number of individuals in the study = Number of individuals who died from cancer + Number of individuals who did not die from cancer
= 973 + (Never smoked cigars + Former cigar smoker + Current cigar smoker) + (Never smoked cigars + Former cigar smoker + Current cigar smoker)
= 973 + (777 + 88 + 108) + (121,312 + 6,168 + 9,684)
= 973 + 973 + 137,164
= 139,110
Finally, let's calculate the probability:
Probability = (Number of individuals who died from cancer or were current cigar smokers) / (Total number of individuals in the study)
= (973 + 108) / 139,110
= 1,081 / 139,110
≈ 0.007779
Therefore, the probability that an individual randomly selected from this study died from cancer or was a current cigar smoker is approximately 0.007779 or 0.7779%.