In a certain town,25% of families own a phone | vedclass

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(C) Let $P$ be the set of families owning a phone and $C$ be the set of families owning a car.Given: $n(P) = 25\%$,$n(C) = 15\%$,and $n(P^c \cap C^c)

Vedclass · Accepted Answer

$2$ and $3$

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(C) Let $P$ be the set of families owning a phone and $C$ be the set of families owning a car.Given: $n(P) = 25\%$,$n(C) = 15\%$,and $n(P^c \cap C^c) = 65\%$.We know that $n(P^c \cap C^c) = n((P \cup C)^c) = 100\% - n(P \cup C)$.Therefore,$n(P \cup C) = 100\% - 65\% = 35\%$. This confirms statement $2$ is correct.Using the formula $n(P \cup C) = n(P) + n(C) - n(P \cap C)$:$35\% = 25\% + 15\% - n(P \cap C)$.$n(P \cap C) = 40\% - 35\% = 5\%$.Since $5\%$ of the total families $= 2000$,the total number of families $= \frac{2000 	imes 100}{5} = 40,000$. This confirms statement $3$ is correct.Statement $1$ claims $10\%$ own both,which is incorrect as we calculated $5\%$.Thus,statements $2$ and $3$ are correct.

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