In a certain town, 25% of the families own a phone and 15% own a car; 65% families own nei…

Question

In a certain town, 25\% of the families own a phone and 15\% own a car; 65\% families own neither a phone nor a car, and 2,000 families own both a car and a phone. Consider the following three statements:

(A) 5\% families own both a car and a phone

(B) 35\% families own either a car or a phone
(C) 40,000 families live in the town

Then:

Accepted Answer

$n(P)=25\%$, $n(C)=15\%$, $n(P\cup C)' = 65\% \Rightarrow n(P\cup C)=35\%$ --- confirms (B).

$n(P\cap C) = n(P)+n(C)-n(P\cup C) = 25+15-35 = 5\%$ --- confirms (A).

If $5\%$ of total families $=2000$, then total $=40000$ --- confirms (C).

All three statements are correct.

Solutions · 1