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

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Question

(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 $3$

Vedclass · Answer

(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 $n(P^c \cap C^c) = 65\%$.Since $n(P^c \cap C^c) = 65\%$,the percentage of families owning at least one (phone or car) is $n(P \cup C) = 100\% - 65\% = 35\%$.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\%$.Thus,statement $1$ is incorrect because $5\%$,not $10\%$,of families own both.Statement $2$ is correct because $n(P \cup C) = 35\%$.Since $5\%$ of the total families $= 2000$,the total number of families $= (2000 / 5) 	imes 100 = 40,000$.Thus,statement $3$ is correct.Therefore,statements $2$ and $3$ are correct.

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