Question

in a certain community it is known that 30% of people born overseas and that 20% of people are smokers. can we conclude that 50% of people in the community were born overseas or are smokers? explain your answer as yes or no in a paragraph of 5 sentences

Answer 1

The total population makes up to 100%. Let O = Event that a person is born overseas S = Event that the person is a smoker

Given: P(S) = 20% = 0.2, P(O) = 30% = 0.3

By Addition theorem of Probability, for two events A and B:

Substituting, we get the formula for required probability as:

= 0.3 + 0.2 - P(OS)

where P(OUS) = Probability that  people in the community were born overseas or are smokers P(OS) =  Probability that  people in the community were born overseas and are smokers

We find that the required probability P(OUS) would be 50% only if the term P(OS), is zero. P(OS) is the probability of intersection of the events O and S. A probability of intersection term can be zero only if the two events are mutually exclusive i. e. the occurance of one event prevents the occurance of the other (the two events can never occur simultaneously).

Hence, we may conclude that 50% of people in the community were born overseas or are smokers only if the person being born overseas and him being a smoker are mutually exclusive events.