In a certain school,74 % of students like cri | vedclass

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Question

(B) Let $C, F,$ and $T$ be the sets of students who like cricket,football,and tennis,respectively.Given: $n(C) = 74 \%$,$n(F) = 76 \%$,$n(T) = 82 \%$.

Vedclass · Accepted Answer

$32$

Vedclass · Answer

(B) Let $C, F,$ and $T$ be the sets of students who like cricket,football,and tennis,respectively.Given: $n(C) = 74 \%$,$n(F) = 76 \%$,$n(T) = 82 \%$.The percentage of students who do not like these sports are:$n(C^c) = 100 \% - 74 \% = 26 \%$$n(F^c) = 100 \% - 76 \% = 24 \%$$n(T^c) = 100 \% - 82 \% = 18 \%$Using the principle of inclusion-exclusion for the complement sets,the percentage of students who do not like at least one sport is at most $n(C^c) + n(F^c) + n(T^c) = 26 \% + 24 \% + 18 \% = 68 \%$.The percentage of students who like all three sports is at least $100 \% - (n(C^c) + n(F^c) + n(T^c)) = 100 \% - 68 \% = 32 \%$.

In a certain school,$74 \%$ of students like cricket,$76 \%$ of students like football,and $82 \%$ of students like tennis. Then,all three sports are liked by at least $...... \%$ of students.

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