In a recent survey of local businessmen and businesswomen, 40% of the respondents belong to the Rotary Club, 70% belong to the Chamber of Commerce.30% were members of both.What proportion of the respondents are members of at least one of the groups?
A).12
B).28
C).9
D).7
E).8

Question

Quizplus · Accepted Answer

To find the proportion of respondents who are members of at least one of the groups, we use the principle of inclusion-exclusion. The formula is: $$ \text{At least one} = \text{Rotary Club} + \text{Chamber of Commerce} - \text{Both} $$Given that 40% belong to the Rotary Club, 70% belong to the Chamber of Commerce, and 30% belong to both, we have:$$ \text{At least one} = 40\% + 70\% - 30\% = 80\% $$To convert this percentage into the options provided (assuming they represent proportions in some form), 80% corresponds to 8 out of 10, or simply 8, which matches option E.

In a Recent Survey of Local Businessmen and Businesswomen, 40