79. As a result of a recent survey conducted by a public health office, it was estimated that 85% of a targeted population enjoys an alcoholic beverage at least once a week; 35% of the population smokes at least one cigarette a day; and 25% of the population indulges in both habits. What is the probability that an individual chosen at random from the targeted population either smokes, or drinks alcohol?
Is it .85+.35-.25=95% because that seems really high
Is it .85+.35-.25=95% because that seems really high
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There are 4 groups of people:
alcohol only = 85 - 25 = 60
smokes only = 35 - 25 = 10
both = 25
neither = 100 - 60 - 10 - 25 = 5
Total of the first three = 95% which you arrived at via a shorter route.
That shouldn't strike you as "really high",
because "alcohol alone" = 85 (including the smokers who drink),
hence the answer must be *at least* that, just to begin with,
which only leaves a small universe (85 - 100) of possibilities.
alcohol only = 85 - 25 = 60
smokes only = 35 - 25 = 10
both = 25
neither = 100 - 60 - 10 - 25 = 5
Total of the first three = 95% which you arrived at via a shorter route.
That shouldn't strike you as "really high",
because "alcohol alone" = 85 (including the smokers who drink),
hence the answer must be *at least* that, just to begin with,
which only leaves a small universe (85 - 100) of possibilities.