(C) Let the total population be $100$.$n(A) = 25$,$n(B) = 20$,and $n(A \cap B) = 8$.Number of people who read $A$ but not $B$ is $n(A \setminus B) = n

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(C) Let the total population be $100$.$n(A) = 25$,$n(B) = 20$,and $n(A \cap B) = 8$.Number of people who read $A$ but not $B$ is $n(A \setminus B) = n(A) - n(A \cap B) = 25 - 8 = 17$.Number of people who read $B$ but not $A$ is $n(B \setminus A) = n(B) - n(A \cap B) = 20 - 8 = 12$.Number of people who read both $A$ and $B$ is $n(A \cap B) = 8$.Percentage of population who look into advertisements:$= (30\% \text{ of } 17) + (40\% \text{ of } 12) + (50\% \text{ of } 8)$$= (0.30 \times 17) + (0.40 \times 12) + (0.50 \times 8)$$= 5.1 + 4.8 + 4.0 = 13.9$.

Class 11 Mathematics Set Theory Word Problem - Set Theory

Difficult

Two newspapers $A$ and $B$ are published in a city. It is known that $25\%$ of the city population reads $A$ and $20\%$ reads $B$,while $8\%$ reads both $A$ and $B$. Further,$30\%$ of those who read $A$ but not $B$ look into advertisements,$40\%$ of those who read $B$ but not $A$ look into advertisements,and $50\%$ of those who read both $A$ and $B$ look into advertisements. The percentage of the population who look into advertisements is:

JEE MAIN 2019 All JEE MAIN

A
$12.8$
B
$13.5$
C
$13.9$
D
$13$

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Let $A = \{1, 2, 3, 4, 5, 6, 7\}$ and $B = \{3, 6, 7, 9\}$. Then the number of elements in the set $\{ C \subseteq A : C \cap B \neq \phi \}$ is

MediumJEE MAIN 2022

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In a class of $125$ students,$70$ passed in Mathematics,$55$ in Statistics,and $30$ in both. The probability that a student selected at random from the class has passed in only one subject is

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An electronic assembly consists of two subsystems,$A$ and $B$. From previous testing procedures,the following probabilities are known:
$P(A \text{ fails}) = 0.2$
$P(B \text{ fails alone}) = 0.15$
$P(A \text{ and } B \text{ fail}) = 0.15$
Evaluate the probability $P(A \text{ fails alone})$.

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The probability that at least one of the events $A$ and $B$ occurs is $0.6$. If $A$ and $B$ occur simultaneously with probability $0.2$,then $P(A') + P(B')$ is equal to

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Let $S = \{1, 2, 3, \ldots, 2022\}$. The probability that a randomly chosen number $n$ from the set $S$ satisfies $\operatorname{HCF}(n, 2022) = 1$ is:

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Let $A = \{1, 2, 3, 4, 5, 6, 7\}$ and $B = \{3, 6, 7, 9\}$. Then the number of elements in the set $\{ C \subseteq A : C \cap B \neq \phi \}$ is

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An electronic assembly consists of two subsystems,$A$ and $B$. From previous testing procedures,the following probabilities are known:
$P(A \text{ fails}) = 0.2$
$P(B \text{ fails alone}) = 0.15$
$P(A \text{ and } B \text{ fail}) = 0.15$
Evaluate the probability $P(A \text{ fails alone})$.